Talking to me?

Lexicographically earliest sequence of nonnegative terms such that the last digit of a(n) is present in a(n+1) 

[corrected by Giorgos Kalogeropoulos and extended –red numbers– by Scott Shannon – this is now A370400 in the OEIS]:

S = 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 1, 11, 12, 2, 21, 13, 3, 23, 31, 14, 4, 24, 34, 41, 15, 5, 25, 35, 45, 51, 16, 6, 26, 36, 46, 56, 61, 17, 7, 27, 37, 47, 57, 67, 71, 18, 8, 28, 38, 48, 58, 68, 78, 81, 19, 9, 29, 39, 49, 59, 69, 79, 89, 91, 102, 22, 32, 42, 52, 62, 72, 82, 92, 112, 120, 103, 33, 43, 53, 63, 73, 83, 93, 113, 123, 130, 104, 44, 54, 64, 74, 84, 94, 114, 124, 134, 140, 105, 55, 65, 75, 85, 95, 115, 125, 135, 145, 150, 106, 66, 76, 86, 96, 116, 126, 136, 146, 156, 160, 107, 77, 87, 97, 117, 127, 137, 147, 157, 167, 170, 108, 88, 98, 118, 128, 138, 148, 158, 168, 178, 180, 109, 99, 119, 129, 139, 149, 159, 169, 179, 189, 190, 110, 200, 201, 111, 121, 122, 132, 142, 152, 162, 172, 182, 192, 202, 203, 131, 133, 143, 153, 163, 173, 183, 193, 213, 223, 230, 204, 141, 144, 154, 164, 174, 184, 194, 214, 224, 234, 240, 205, 151, 155, 165, 175, 185, 195, 215, 225, 235, 245, 250, 206, 161, 166, 176, 186, 196, 216, 226, 236, 246, 256, 260, 207, 171, 177, 187, 197, 217, 227, 237, 247, 257, 267, 270, 208, 181, 188, 198, 218, 228, 238, 248, 258, 268, 278, 280, 209, 191, 199, 219, 229, 239, 249, 259, 269, 279, 289, 290, 210, 220, 300, 301, 211, 212, 221, 231, 241, 251, 261, 271, 281, 291, 310, 302, 222, 232, 233, 243, 253, 263, 273, 283, 293, 303, 304, 242, 244, 254, 264, 274, 284, 294, 314, 324, 334, 340, 305, 252, 255, 265, 275, 285, 295, 315, 325, 335, 345, 350, 306, 262, 266, 276, 286, 296, 316, 326, 336, 346, 356, 360, 307, 272, 277, 287, 297, 317, 327, 337, 347, 357, 367, 370, 308, 282, 288, 298, 318, 328, 338, 348, 358, 368, 378, 380, 309, 292, 299, 319, 329, 339, 349, 359, 369, 379, 389, 390, 320, 330, 400, 401, 311, 312, 321, 313, 322, 323, 331, 341, 351, 361, 371, 381, 391, 410, 402, 332, 342, 352, 362, 372, 382, 392, 412, 420, 403, 333, 343, 344, 354, 364, 374, 384, 394, 404, 405, 353, 355, 365, 375, 385, 395, 415, 425, 435, 445, 450, 406, 363, 366, 376, 386, 396, 416, 426, 436, 446, 456, 460, 407, 373, 377, 387, 397, 417, 427, 437, 447, 457, 467, 470, 408, 383, 388, 398, 418, 428, 438, 448, 458, 468, 478, 480, 409, 393, 399, 419, 429, 439, 449, 459, 469, 479, 489, 490, 430, 440, 500, 501, 411, 413, 423, 431, 414, 421, 441, 451, 461, 471, 481, 491, 510, 502, 422, 424, 432, 442, 452, 462, 472, 482, 492, 512, 520, 503, 433, 434, 443, 453, 463, 473, 483, 493, 513, 523, 530, 504, 444, 454, 455, 465, 475, 485, 495, 505, 506, 464, ...

Lexicographically earliest sequence of nonnegative terms such that the first digit of a(n) is present in a(n+1) [this is now A370401 in the OEIS]:

T = 0, 10, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 2, 20, 22, 23, 24, 25, 26, 27, 28, 29, 32, 3, 30, 31, 33, 34, 35, 36, 37, 38, 39, 43, 4, 40, 41, 42, 44, 45, 46, 47, 48, 49, 54, 5, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 6, 60, 61, 62, 63, 64, 66, 67, 68, 69, 76, 7, 70, 71, 72, 73, 74, 75, 77, 78, 79, 87, 8, 80, 81, 82, 83, 84, 85, 86, 88, 89, 98, 9, 90, 91, 92, 93, 94, 95, 96, 97, 99, 109, 100, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, ...

Lexicographically earliest sequence of nonnegative terms such that the last digit of a(n) is present in a(n+1) and the last letter of the English name of a(n) is present in the English name of a(n+1) [corrected and extended by GK – this is now A370402 in the OEIS]:

U = 0, 40, 20, 30, 50, 60, 70, 80, 90, 120, 130, 140, 150, 160, 170, 180, 190, 220, 230, 240, 250, 260, 270, 280, 290, 320, 330, 340, 350, 360, 370, 380, 390, 420, 430, 440, 450, 460, 470, 480, 490, 520, 530, 540, 550, 560, 570, 580, 590, 620, 630, 640, 650, 660, 670, 680, 690, 720, 730, 740, 750, 760, 770, 780, 790, 820, 830, 840, 850, 860, ...

U = 0 zero, 40 forty, 20 twenty, 30 thirty, 50 fifty, 60 sixty, 70 seventy, 80 eighty, 90 ninety, 120 one hundred twenty, 130 one hundred thirty, 140 one hundred forty, 150 one hundred fifty, 160 one hundred sixty, 170 one hundred seventy, 180 one hundred eighty, 190 one hundred ninety, 220 two hundred twenty, 230 two hundred thirty, 240 two hundred forty, 250 two hundred fifty, 260 two hundred sixty, 270 two hundred seventy, 280 two hundred eighty, 290 two hundred ninety, 320 three hundred twenty, 330 three hundred thirty, 340 three hundred forty, 350 three hundred fifty, 360 three hundred sixty, 370 three hundred seventy, 380 three hundred eighty, 390 three hundred ninety, ...

Lexicographically earliest sequence of positive integers such that the first digit of a(n) is present in a(n+1) and the first letter of the English name of a(n) is present in the English name of a(n+1) [corrected and extended by GK – this is now A370403 in the OEIS]:

V = 1, 14, 15, 41, 4, 24, 2, 12, 10, 13, 16, 17, 61, 6, 26, 20, 21, 22, 23, 25, 27, 28, 29, 32, 3, 30, 31, 33, 34, 35, 36, 37, 38, 39, 43, 40, 42, 44, 45, 46, 47, 48, 49, 54, 5, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 60, 62, 63, 64, 66, 67, 68, 69, 76, 7, 70, 71, 72, 73, 74, 75, 77, 78, 79, 87, 8, 18, 11, 19, 81, 80, 82, 83, 84, 85, 86, 88, 89, 98, 9, 90, 91, 92, 93, 94, 95, 96, 97, 99, 109...

V = 1 one, 14 fourteen, 15 fifteen, 41 forty-one, 4 four, 24 twenty-four, 2 two, 12 twelve, 10 ten 13 thirteen, 16 sixteen, 17 seventeen, 61 sixty-one, 6 six, 26 twenty-six, 20 twenty, 21 twenty-one, 22 twenty-two, 23 twenty-three, 25 twenty-five, 27 twenty-seven, 28 twenty-eight, 29 twenty-nine, 32 thirty-two, 3 three, 30 thirty, 31 thirty-one, 33 thirty-three, 34 thirty-four, 35 thirty-five, 36 thirty-six, 37 thirty-seven, 38 thirty-eight, 39 thirty-nine, 43 forty-three, 40 forty, 42 forty-two, 44 forty-four, 45 forty-five, 46 forty-six, 47 forty-seven, 48 forty-eight, 49 forty-nine, 54 fifty-four, 5 five, 50 fifty, ...

Lexicographically earliest sequence of nonnegative terms such that the last digit of a(n) is present in a(n+1), the last letter of the English name of a(n) is present in the English name of a(n+1) and the last letter of the French name of a(n) is present in the French name of a(n+1) [corrected and extended by GK – this is now A370404 in the OEIS]:

W = 0, 103, 3, 23, 33, 37, 7, 17, 27, 47, 57, 67, 70, 60, 30, 40, 50, 80, 160, 90, 170, 190, 220, 20, 120, 130, 140, 150, 180, 260, 230, 240, 250, 270, 280, 320, 290, 360, 330, 340, 350, 370, 390, 460, 380, 470, 490, 560, 420, 430, 440, 450, 480, 570, 590, 620, 520, 530, 540, 550, 580, 630, 640, 650, 660, 670, 680, 690, 760, 720, 730, 740, 750, 770, 790, 860, 780, 870, 890, 960, 820, 830, 840, 850, 880, 970, 990, 1022, 2, 22, 32, 42, 52, 62, 72, 21, 1, 11, 13, 31, 15, 51, 19, 9, 29, 39, 49, 59, 69, 79, 89, 99, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 209, 219, 229, 239, 249, 259, 269, 279, 289, 299, 309, 319, 329, 339, 349, 359, 369, 379, 389, 399, 409, 419, 429, 439, 449, 459, 469, 479, 489, 499, 509, 519, 529, 539, 549, 559, 569, 579, 589, 599, 609, 619, 629, 639, 649, 659, 669, 679, 689, 699, 709, 719, 729, 739, 749, 759, 769, 779, 789, 799, 809, 819, 829, 839, 849, 859, 869, 879, 889, 899, 900, 106, 6, 26, 36, 46, 56, 61, ...

0    zero                  zéro

103  one hundred three     cent trois

3    three                 trois

23   twenty-three          vingt-trois

33   thirty-three          trente-trois

37   thirty-seven          trente-sept

7    seven                 sept

17   seventeen             dix-sept

27   twenty-seven          vingt-sept

47   forty-seven           quarante-sept

57   fifty-seven           cinquante-sept

67   sixty-seven           soixante-sept

70   seventy               soixante-dix

60   sixty                 soixante

30   thirty                trente

40   forty                 quarante

50   fifty                 cinquante

80   eighty                quatre-vingts

160  one hundred sixty     cent soixante

90   ninety                quatre-vingt-dix

170  one hundred seventy   cent soixante-dix

190  one hundred ninety    cent quatre-vingt-dix

220  two hundred twenty    deux cent vingt

20   twenty                vingt

120  one hundred twenty    cent vingt 

130 one hundred thirty     cent trente

140 one hundred forty      cent quarante

150 one hundred fifty      cent cinquante

180 one hundred eighty     cent quatre-vingts

260  two hundred sixty     deux cent soixante

230  two hundred thirty    deux cent trente

240  two hundred forty     deux cent quarante

250  two hundred fifty     deux cent cinquante

270  two hundred seventy   deux cent soixante-dix

280  two hundred eighty    deux cent quatre-vingts

320  three hundred twenty  trois cent vingt

290  two hundred ninety    deux cent quatre-vingt-dix

...

Lexicographically earliest sequence of positive terms such that the first digit of a(n) is present in a(n+1), the first letter of the English name of a(n) is present in the English name of a(n+1) and the first letter of the French name of a(n) is present in the French name of a(n+1) [this is now A370405]:

X = 1, 14, 15, 41, 4, 24, 20, 21, 22, 23, 25, 26, 27, 28, 29, 82, 48, 34, 3, 13, 17, 117, 51, 5, 35, 30, 31, 32, 33, 36, 37, 38, 39, 43, 40, 42, 44, 45, 46, 47, 49, 54, 50, 52, 53, 55, 56, 57, 58, 59, 65, 6, 16, 61, 60, 62, 63, 64, 66, 67, 68, 69, 76, 7, 70, 71, 72, 73, 74, 75, 77, 78, 79, 87, 80, 81, 83, 84, 85, 86, 88, 89, 98, 90, 91, 92, 93, 94, 95, 96, 97, 99, 149, 100, 101, 102, 103, 104, 105, 106, ...

____________________

Many thanks to Giorgos and Scott!

(Dall-e creation)