A034293 Numbers k such that 2^k does not contain the digit 2 (probably finite).

0, 2, 3, 4, 6, 12, 14, 16, 20, 22, 23, 26, 34, 35, 36, 39, 42, 46, 54, 64, 74, 83, 168

Offset

1,2

Comments

Is 168 the last term?

First row of A136291. - R. J. Mathar Apr 29 2008

Equivalently, indices of zeros in A065710. - M. F. Hasler, Feb 10 2023

Links

Table of n, a(n) for n=1..23.

Formula

The last term is A094776(2), by definition. - M. F. Hasler, Feb 10 2023

Example

Here is 2^168, conjecturally the largest power of 2 that does not contain a 2:
374144419156711147060143317175368453031918731001856. - N. J. A. Sloane, Feb 10 2023

Maple

isA034293 := proc(n) RETURN(not 2 in convert(2^n, base, 10)) ; end: for n from 0 to 100000 do if isA034293(n) then print(n) ; fi ; od: # R. J. Mathar, Oct 04 2007

Mathematica

Join[{0}, Select[ Range@10000, FreeQ[ IntegerDigits[2^# ], 2] &]] (* Shyam Sunder Gupta, Sep 01 2007 *)(* adapted by Vincenzo Librandi, May 07 2015 *)
Select[Range[0, 10^4], DigitCount[2^#][[2]] == 0 &] (* Michael De Vlieger, Apr 29 2016 *)

Prog

(Magma) [n: n in [0..1000] | not 2 in Intseq(2^n) ]; // Vincenzo Librandi, May 07 2015
(PARI) is(n)=setsearch(Set(digits(2^n)), 2)==0 \\ Charles R Greathouse IV, May 10 2016
(PARI) is_A034293(n)=!foreach(digits(2^n), d, d==2&&return) \\ M. F. Hasler, Feb 10 2023
(Python)
def is_A034293(n): return'2'not in str(2**n)
[n for n in range(199) if is_A034293(n)] # M. F. Hasler, Feb 10 2023

Crossrefs

Cf. A007377.

See also similar sequences listed in A035064.

Cf. A065710, A094776.

Sequence in context: A018309 A245481 A039038 * A136291 A128393 A368988

Adjacent sequences: A034290 A034291 A034292 * A034294 A034295 A034296

Keyword

base,nonn

Author

Erich Friedman

Extensions

Edited by N. J. A. Sloane, Oct 03 2007

Removed keyword "fini" since it is only a conjecture that this sequence contains only finitely many terms. - Altug Alkan, May 07 2016

Status

approved