Another brick (in the wall)
Now we would like to make bricks (to throw them in Putin's face?) By superimposing two numbers in a «correct» way.
This is for instance a 2-integer brick we accept:
1291951
9371733
9371733
Why? Because, when we read vertically, we encounter only prime numbers. They are (left to right):
19, 23, 97, 11, 97, 53, 13.
Note that neither 1291951, nor 9371733 are primes – we
are only interested in vertical 2-digit (sometimes 1-digit) primes.
Here are four bricks we accept – and four we don’t:
We accept:
a b c d
391 213 37 13973
We reject:
e f g h
14 17 413 235678980
191 913 17 139735
Why?
a:
the leftmost vertical integer is seen here as the prime “3” – the next two are
19 and 41;
How about a brick-sequence?
Definition: lexicographically earliest sequence of distinct
positive integers such that a(n) written on top of a(n+1) forms an accepted 2-integer
brick.
S = 1,3,7,9,27,31,11,71,91,73,17,19,37,13,77,33,211,39,217,93,271,97,273,311,79,237,313,111,113,117,119,137,171,131,173,191,133,317,…
February 28th 2022 update
Carole D. has corrected my start and computed this new one:
S = 1, 3, 7, 9, 27, 31, 11, 13, 17, 19, 37, 71, 33, 77, 39, 217, 73, 91, 79, 97, 271, 93, 277, 99, 377, 111, 113, 117, 119, 137, 171, 131, 173, 191, 177, 133, 311, 139, 317, 179, 197, 371, 193, 771, 199, 777, 313, 711, 319, 717, 331, 713, 337, 719, 397, 773, 391, 779, 917, 731, 373, 737, 379, 797, 971, 733, 911, 739, 977, 791, 973, 2711, 333, 2111, 339, 2117, 393, 2171, 399, 2177, 793, 2371, 799, 2377, 3111, 913, 2717, 919, 2737, 979, 2797, 3171, 931, 2713, 937, 2719, 997, 2771, 933, 2777, 939, 3717, 991, 2773, 3117, 993, 3771, 999, 3777, 1111, 1113, 1117, 1119, 1137, 1171, 1131, 1173, 1191, 1177, 1133, 1311, 1139, 1317, 1179, 1197, 1371, 1193, 1377, 1199, 1777, 1313, 1711, 1319, 1717, 1331, 1713, 1337, 1719, 1397, 1771, 1333, 3177, 1339, 7117, 1373, 1731, 1379, 1737, 1911, 1733, 1917, 1739, 1977, 1791, 1971, 1793, 3371, 1797, 1973, 3711, 1391, 1773, 1931, 1779, 1937, 3713, 1991, 3773, 1997, 3779, 7137, 1913, 3731, 1919, 3737, 1979, 3797, 7171, 1393, 7177, 1399, 7777, 1933, 7711, 1939, 7717, 1993, 7771, 1999, 9777, 7111, 1799, 3377, 7113, 3131, 7119, 3137, 7173, 3191, 7179,...
Carole asks: "What about 3-layer bricks?"
T = 1, 2, 7, 21, 9, 3, 27, 33, 39, 17, 11, 239, 13, 37, 19, 77, 31, 99, 71, 79, 231, 91, 73, 211, 93, 97, 213, 313, 331, 111, 113, 337, 119, 117, 2331, 179, 131, 339, 171, 139, 333, 177, 133, 393, 771, 311, 993, 711, 191, 913, 197, 173, 319, 797, 317, 2313, 733, 371, 391, 773, 377, 933, 739, 717, 2311, 939, 713, 137, 919, 737, 777, 2333, 399, 3177, 1111, 1399, 193, 1117, 1313, 3133, 397, 779, 917, 791, 199, 911, 719, 731, 379, 931, 799, 2171, 971, 3333, 1731, 373, 1331, 1131, 3113, 1311, 937, 1713, 1113, 3931, 793, 1171, 1911, 3193, 977, 973, 2133, 991, 3171, 1173, 1337, 999, 1777, 1177, 3933, 1133, 1917, 979, 1137, 1191, 3379, 1119, 1197, 3311, 1199, 1139, 3371, 1739, 997, 1771, 1179, 3937, 1391, 1779, 3313, 1397, 1193, 3119, 1317, 1737, 3373, 1333, 1791, 3377, 1319, 1797, 3317, 1393, 1719, 3397, 1371, 3179, 1339, 1931, 3711, 1733, 1377, 3339, 7137, 3111, 3319, 1933, 1717, 3139, 1977, 1937, 3733, 1773, 3331, 1991, 3773, 1711, 3391, 1373, 3117, 1793, 1379, 3917, 7791, 3199, 3911, 1799, 3131, 1971, 1993, 3771, 7111, 3993, 3137, 1973, 1939, 3197, 7171, 9319, 7191, 7119,...
Explanation:
1,2,7 are ok because 127 is prime;
2, 7, 21 are ok because 271 and 2 are prime numbers;
7, 21, 9 are ok because 719 and 2 are prime numbers;
....
1739, 997, 1771 are ok because 971, 397, 797, 11 are prime numbers:
1739
997
1771
Perfect, Carole, thanks! This will be submitted soon to the OEIS!
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