A376856 a(1) = 1; for n > 1, a(n) is the smallest unused positive number such that a(n), |a(n) - a(n-1)| and a(1) + ... +a(n) are all palindromes.

1, 2, 3, 5, 11, 22, 33, 44, 121, 222, 101, 202, 454, 1221, 2222, 1001, 2002, 4554, 12221, 22222, 10001, 20002, 45554, 122221, 222222, 100001, 200002, 455554, 1222221, 2222222, 1000001, 2000002, 4555554, 12222221, 22222222, 10000001, 20000002, 45555554, 122222221, 222222222, 100000001, 200000002, 455555554, 1222222221, 2222222222, 1000000001

Offset

1,2

Comments

The sequence is infinite as from a(13) onward a repetitive pattern of five numbers appears, 45...54, 12...21, 22...22, 10...01, 20...02, all of which grow by one extra digit each iteration.

Links

Table of n, a(n) for n=1..46.

Example

a(9) = 121 as 121 is a palindrome, |121 - 44| = 77 is a palindrome, and 1 + 2 + 3 + 5 + 11 + 22 + 33 + 44 + 121 = 242 is a palindrome.

Crossrefs

Cf. A073880, A073879, A002113, A369127, A361335, A347402.

Sequence in context: A117221 A073879 A073880 * A118332 A118333 A131101

Adjacent sequences: A376853 A376854 A376855 * A376857 A376858 A376859

Keyword

nonn,base

Author

Scott R. Shannon, Oct 06 2024

Status

approved