cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A361336 Smallest decimal number containing n palindromic substrings (Version 2). See Comments for precise definition.

Original entry on oeis.org

0, 10, 11, 100, 1002, 111, 1000, 10002, 10001, 1111, 10000, 100002, 100001, 1000012, 11111, 100000, 1000002, 1000001, 10000012, 10000010, 111111, 1000000, 10000002, 10000001, 100000012, 100000010, 110111111, 1111111, 10000000, 100000002, 100000001, 1000000012, 1000000010
Offset: 1

Views

Author

N. J. A. Sloane, Apr 01 2023, based on postings to the Sequence Fans Mailing list by Eric Angelini, Mar 28 2023 (definition), and Giovanni Resta, Mar 28 2023 (terms)

Keywords

Comments

Suppose m has decimal expansion d_1 d_2 ... d_k. A palindromic substring here is any substring d_i, d_{i+1}, ..., d_j with 1 <= i <= j <= n which is palindromic. In this version d_i can be 0 even if j>i. For example, if m = 10^3 + 1 = 1001 there are six substrings: 1, 0, 0, 1, 00, and 1001. See A361335 for Version 1.

Links

Crossrefs

Cf. A361335.

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.

Original entry on oeis.org

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

Views

Author

Scott R. Shannon, Oct 06 2024

Keywords

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.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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