A035064 Numbers k such that 2^k does not contain the digit 9 (probably finite).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 30, 31, 45, 46, 47, 57, 58, 59, 71, 77, 99, 108

Offset: 1

Author

Patrick De Geest, Nov 15 1998

Keywords

• nonn
• base

Examples

			Here is 2^108, conjecturally the largest power of 2 that does not contain a 9: 324518553658426726783156020576256. - _N. J. A. Sloane_, Feb 10 2023
		

Crossrefs

Cf. numbers n such that decimal expansion of 2^n contains no k: A007377 (k=0), A035057 (k=1), A034293 (k=2), A035058 (k=3), A035059 (k=4), A035060 (k=5), A035061 (k=6), A035062 (k=7), A035063 (k=8), this sequence (k=9).

Indices of zeros in A065744 (number of 9s in digits of 2^n).

Programs

Magma

[n: n in [0..1000] | not 9 in Intseq(2^n) ]; // Vincenzo Librandi, May 06 2015

Mathematica

Join[{0}, Select[Range@ 1000, FreeQ[IntegerDigits[2^#], 9] &]] (* Vincenzo Librandi, May 06 2015 *)

PARI

A035064 = select( is_A035064(n)=vecmax(digits(2^n))<9, [0..199]) \\ M. F. Hasler, Jul 09 2025

Python

(A035064:=[n for n in range(123) if max(str(2**n))<'9']) # M. F. Hasler, Jul 09 2025

Extensions

Initial 0 added by Vincenzo Librandi, May 06 2015

Removed keyword "fini" at the suggestion of Nathan Fox, since it is only a conjecture that this sequence contains only finitely many terms. - N. J. A. Sloane, Mar 03 2016