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

Author

Scott R. Shannon, Oct 06 2024

Keywords

• nonn
• base

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.

Examples

			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.