A052057 Numbers k such that the decimal expansion of 2^k contains no palindromic substring except single digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 29, 37, 54

Offset: 1

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base
• more

Comments

Sequence is probably finite. Next term, if it exists, exceeds 1170.

Next term, if it exists, exceeds 50000. - Sean A. Irvine, Oct 18 2021

Examples

			Record number is 2^54 = 18014398509481984.
		

Crossrefs

Cf. A000079, A050723, A052058, A052059.

Programs

Mathematica

Select[Range[0, 10^3], NoneTrue[DeleteCases[Subsequences@ IntegerDigits[2^#], ?(Length[#] <= 1 &)], PalindromeQ] &] (* _Michael De Vlieger, Oct 18 2021 *)

Extensions

Edited by Jon E. Schoenfield, Oct 17 2019