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

Author

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

Keywords

• nonn
• base

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).

Examples

			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.
		

Links

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

Crossrefs

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