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

1,3

Links

Table of n, a(n) for n=1..37.

Example

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

Mathematica

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

Prog

(Magma) [n: n in [0..1000] | not 9 in Intseq(2^n) ]; // 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

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).

Sequence in context: A048336 A130574 A023780 * A113191 A191923 A191922

Adjacent sequences: A035061 A035062 A035063 * A035065 A035066 A035067

Keyword

nonn,base,more

Author

Patrick De Geest, Nov 15 1998

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

Status

approved