More digits, terms and primes

I've just rediscovered (and recomputed by hand) the first terms of A281878, which had been already submitted to the OEIS 7 years ago by Jean-Marc Falcoz and the author:

NAME

The sum of two successive terms is prime and the sum of two successive digits is also prime.

DATA

S = 0, 2, 1, 4, 3, 8, 5, 6, 7, 412, 9, 20, 21, 16, 111, 112, 121, 120, 29, 212, 11, 12, 125, 234, 149, 230, 203, 216, 143, 258, 305, 252, 167, 432, 161, 116, 123, 214, 165, 202, 129, 238, 303, 298, 321, 250, 207, 434, 323, 294, 307, 612, 325, 232, 141, 256, 505, 292, 147, 416, 503, 438, 349, 474, 347, 414, 329, 492, 385, 676, 525, 656, 507,...

What about the analog sequence T, replacing "sum" by "absolute difference"? We would then have:

NAME

The absolute difference of two successive terms is prime and the absolute difference of two successive digits is also prime.

DATA

T = 0, 2, 4, 1, 3, 5, 7, 9, 6, 8, 13, 16, 14, 25, 20, 27, 24, 29, ...

______________

Same day update 

Jean-Marc Falcoz quickly computed 20,000 terms for T and submitted the hereunder nice graph: merci Jean-Marc, this is now in the OEIS!

T ={0,2,4,1,3,5,7,9,6,8,13,16,14,25,20,27,24,29,42,47,49,46,35,30,53,50,31,36,38,57,52,41,64,61,63,58,69,72,70,75,86,81,68,135,74,79,242,469,246,83,85,252,425,202,413,130,203,136,131,358,147,94,92,97,270,241,302,429,250,207,205,258,149,418,141,314,163,146,169,272,463,186,181,318,161,352,461,364,183,142,479,420,247,96,185,274,257,294,253,164,613,524,297,292,503,505,368,307,296,303,502,497,414,275,316,305,702,475,386,313,536,357,416,363,520,249,472,470,279,616,353,586,813,530,381,350,361,464,631,468,385,383,574,635,724,641,474,647,424,681,614,685,746,835,752,525,758,369,496,494,705,703,572,529,492,535,792,581,618,575,742,531,638,507,538,527,570,583,585,796,857,924,683,630,727,920,729,646,869,636,863,696,427,968,579,686,853,642,725,720,707,946,927,925,794,697,974,741,694,692,753,814,747,970,797,964,941,838,1305,818,1381,858,1307,2050,749,2038,1361,852,949,750,757,2036,975,836,831,850,2031,830,2053,816,929,2020,2025,2027,2024,961,864,947,942,979,2030,2035,2052,4135,2072,963,1316,969,2416,1313,1302,4163,1386,1303,1314,1357,2058,649,2472,4141,3024,1427,2070,2029,2418,1369,2420,2413,1350,2479,2468,1429,2492,4149,2530,2427,2074,1383,1352,4185,2464,1413,1416,1363,1358,1353,1364,1425,868,1461,3020,2079,2536,1385,2424,1613,1414,1475,2494,1463,1420,2429,2470,2463,1424,1497,2474,1635,2572,4131,3038,1479,2570,2461,3030,2507,2496,1685,2524,1641,3050,2503,1464,1469,2502,4169,2586,1649,2742,4181,3052,4161,3058,1631,3070,2057,2520,2497,2414,1681,3164,1683,1472,4183,1470,2531,3072,4253,1636,1638,1697,2574,1813,1496,1494,1492,4203,1474,1647,2750,2469,2702,4635,2746,1835,2964,1861,3074,1857,2720,2527,2525,2538,3025,2792,4275,2752,4205,2724,2575,2924,1831,3138,3029,2758,3027,2794,1853,1614,1616,1618,1869,2920,2583,1630,2727,2725,2796,3035,2946,3053,1686,3169,2942,4249,2970,2581,3168,3031,3036,3079,2972,4279,4130,2529,2968,3057,2974,2475,3136,3075,3142,4613,1642,4641,3130,2729,4138,3141,3146,1863,1696,1694,1692,4241,3502,4631,3538,3149,4146,3163,1836,1838,3135,3524,2505,3536,3147,4168,3185,3183,1816,1814,2797,4164,2075,3574,2535,3586,3503,5052,4685,3186,3181,3530,2703,1850,2707,2705,3616,3507,4246,3527,4186,3525,3520,2579,4242,4247,4250,2757,4618,3131,3570,2741,3618,3161,3814,2585,3636,3505,3572,4681,3630,2747,2749,4202,4207,4136,3529,4142,4147,4274,2947,2949,4252,4257,4270,2963,5050,2753,5020,3531,3614,2941,3642,4703,1852,4649,4296,3535,3638,3579,4630,2961,3694,2925,2927,2929,4638,3575,3646,3585,3583,1830,3613,5036,3813,1864,6135,3838,3581,3850,2969,4258,3641,3852,4705,3686,3649,4292,4294,2975,3858,3631,3692,4683,1646,3685,3683,5242,4925,3696,3635,3816,3818,3681,3830,3835,3864,2425,7074,6163,5070,3647,4614,6181,4692,4694,6141,3868,3831,3836,3697,4616,4647,4636,3863,5272,4725,7036,3869,4642,4749,4646,4297,4686,3857,4696,4707,4702,4697,4720,2979,4972,4929,4750,5027,4746,4727,4724,6147,4924,6161,4272,4729,4742,4747,4752,4741,4758,5029,4796,4753,5024,6303,5072,4941,4792,4794,6305,7024,6185,7038,5035,7052,4963,5030,5025,7246,4949,4920,5057,4968,5075,7072,4961,4942,4947,4964,6363,5074,6183,5246,4797,4946,3853,5252,4969,4974,6383,5202,4975,7058,5031,4970,3861,6130,5079,6142,4979,6352,5249,6136,8135,7252,5241,6302,5053,5058,5207,5205,7202,5203,5250,5247,5258,5253,5270,5257,5274,6131,6138,5275,7272,5279,6186,4757,5038,5307,5294,6307,5316,4927,5358,5297,5292,5303,5296,8147,5314,6353,5302,5305,7292,5313,5318,5361,6314,6316,8163,5386,8183,5350,5352,5357,5364,6361,6164,6169,6146,8149,6318,5381,6168,5705,7258,5369,6418,5385,7274,6463,5702,5353,5720,5383,5742,5363,5368,5727,5724,6385,7242,5749,6350,5703,5746,8169,6358,5741,6414,6313,5750,5707,5796,8185,7416,8303,5752,5729,6420,5747,5758,5753,5794,6357,5816,8503,5792,5725,7296,8305,7418,5797,5814,6413,5836,8313,6364,6369,6386,8383,5852,5835,7294,6497,5838,5831,6424,6381,6368,5869,6416,8505,7414,6461,6464,6427,5850,5813,5818,5757,5830,5853,5858,5861,6468,6425,7464,6857,9246,8363,6474,6469,6472,7029,6818,6429,6470,5857,5864,6831,6494,6475,7472,5863,5868,6149,6496,8307,9274,6863,6816,8369,6492,7079,6838,6479,6852,7025,7020,7027,9270,7031,6850,7203,6814,6861,6830,7053,6946,8385,7474,6813,6836,8529,6920,7057,9294,6835,7494,6853,6858,6869,6864,6925,7424,6961,6924,6927,9470,7249,6942,7205,7207,9296,8527,9414,6941,6868,6929,6970,7241,6964,6947,9258,6949,6968,6963,6974,6969,6972,7075,7070,7297,9630,7247,9250,7253,8130,7429,7050,7279,7250,7257,9418,13025,7468,13031,8142,7469,7030,7035,7492,7413,8146,8141,8136,8131,8138,6975,7496,8353,8186,8181,8164,7425,7420,7427,9420,7507,9494,7497,9496,8525,7572,7463,8302,7475,7470,7529,7524,7505,7502,7275,7270,7461,8314,7503,8386,8357,9474,7525,7520,7479,7538,13057,9464,7531,8318,13131,8570,7579,7536,8507,9616,8583,8350,7527,9416,8535,7942,7575,7570,7581,8168,13029,7586,8635,7574,7585,7583,8316,8579,7530,7535,7924,7927,9636,8575,7968,13027,9468,13075,7974,7961,8358,13079,7972,7925,7920,7949,7946,8647,9614,7947,9646,8585,8352,7963,8364,7975,7964,7941,8572,7929,7970,20247,9746,8649,20242,7979,20302,9275,8368,13161,8524,9207,9202,9205,8574,9247,9242,9249,20252,9279,20258,1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Robert Indiana, The Sweet Mystery, Venice 2024