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A356822
Irregular triangle read by rows where row n starts with n and each further term is the sum of the distinct palindromes in the concatenation of the decimal digits of preceding terms.
1
1, 1, 12, 125, 463, 476, 483, 491, 500, 500, 6055, 6170, 2, 2, 24, 250, 497, 513, 517, 3, 3, 36, 375, 750, 2082, 2112, 4258, 4504, 4504, 4548, 5002, 4, 4, 48, 500, 505, 6065, 62742, 63407, 63410, 63411, 63422, 63444, 5, 5, 60, 66, 738, 756
OFFSET
1,3
COMMENTS
Palindromes are substrings and 0s are included so that for instance 00500 is a palindrome, and 0 and 00 are distinct (but both value 0).
The first term in the first row is 1, which is a palindrome, so each subsequent term is the sum of all distinct palindromes in the concatenation of the sequence. So far we have 1,1,... This gives us one new palindrome (11), so our new sum is 1+11=12. Now we have 1,1,12,... This added two palindromes (111 and 2) to make the new total 125. Continue until you reach a term which repeats endlessly without adding any new palindromes. For n=1, this term is 6170.
LINKS
Neal Gersh Tolunsky, Table of n, a(n) for n = 1..9324 (first 1000 rows)
EXAMPLE
Irregular array begins:
1, 1, 12, 125, 463, 476, 483, 491, 500, 500, 6055, 6170;
2, 2, 24, 250, 497, 513, 517;
3, 3, 36, 375, 750, 2082, 2112, 4258, 4504, 4504, 4548, 5002;
4, 4, 48, 500, 505, 6065, 62742, 63407, 63410, 63411, 63422, 63444;
5, 5, 60, 66, 738, 756;
6, 6, 72, 81, 90, 99, 1107, 1118, 1229, 1432, 1439;
7, 7, 84, 96, 111, 234, 239;
8, 8, 96, 111, 234, 243, 34910, 39277, 39361, 39754, 39759, 39759, 40698;
9, 9, 108, 117, 135, 314, 14202, 14961, 14967;
10, 1, 102, 225, 474, 959, 1927, 2846, 3132, 3448, 3815, 4653
CROSSREFS
Sequence in context: A155595 A070312 A153427 * A178626 A223322 A061114
KEYWORD
nonn,tabf,look,base
AUTHOR
Neal Gersh Tolunsky, Sep 17 2022
STATUS
approved