A359510 Numbers that can't be written as a palindromic product, i.e., such that the concatenation of all digits of the factors yields a palindrome.

23, 26, 29, 30, 34, 35, 37, 38, 43, 47, 53, 57, 59, 62, 65, 67, 70, 73, 74, 79, 82, 83, 85, 86, 87, 89, 92, 94, 95, 97, 103, 106, 107, 109, 123, 127, 130, 134, 137, 139, 140, 142, 145, 146, 148, 149, 152, 157, 158, 163, 167, 170, 173, 174, 178, 179, 182, 183, 185, 190, 193, 194, 197

Offset

1,1

Comments

Any number of factors 1 is allowed anywhere in the product.

The sequence contains all primes which are not palindromic when stripped of digits '1' on either side (for example 23, 29, 37, but not 13, 17, 19, 31 which can be written as 13*1, 17*1, 19*1, 1*31, etc., where the concatenation of all digits, "131", "171", ... is palindromic).

Links

Table of n, a(n) for n=1..63.

Eric Angelini, 2023 = 7*17*17, a palindromic product, math-fun list (restricted to subscribers), Jan. 1, 2023.

Example

Any palindrome is trivially a palindromic product and therefore not in the sequence. Also not in the sequence are 10 = 10*1, 12 = 12*1, ..., 20 = 2*5*2, 21 = 1*21. Therefore the first term is a(1) = 23.

Crossrefs

Cf. A002113 (palindromes in base 10), A029742 (non-palindromes), A334321 (non-palindromic primes), A004176 (omit digits 1).

Sequence in context: A111452 A335180 A147627 * A345489 A025059 A365020

Adjacent sequences: A359507 A359508 A359509 * A359511 A359512 A359513

Keyword

nonn,base

Author

M. F. Hasler and Eric Angelini, Jan 03 2023

Status

approved