A007377 - OEIS (original) (raw)

A007377

Numbers k such that the decimal expansion of 2^k contains no 0.
(Formerly M0485)

56

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 18, 19, 24, 25, 27, 28, 31, 32, 33, 34, 35, 36, 37, 39, 49, 51, 67, 72, 76, 77, 81, 86

COMMENTS

It is an open problem of long standing to show that 86 is the last term.

See A030700 for the analog for 3^k, which seems to end with k=68. - M. F. Hasler, Mar 07 2014

REFERENCES

J. S. Madachy, Mathematics on Vacation, Scribner's, NY, 1966, p. 126.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Eric Weisstein's World of Mathematics, Zero

EXAMPLE

Here is 2^86, conjecturally the largest power of 2 not containing a 0: 77371252455336267181195264. - N. J. A. Sloane, Feb 10 2023

MAPLE

remove(t -> has(convert(2^t, base, 10), 0), [$0..1000]); # Robert Israel, Dec 29 2015

MATHEMATICA

Do[ If[ Union[ RealDigits[ 2^n ] [[1]]] [[1]] != 0, Print[ n ] ], {n, 1, 60000}]

Select[Range@1000, First@Union@IntegerDigits[2^# ] != 0 &]

Select[Range[0, 100], DigitCount[2^#, 10, 0]==0&] (* Harvey P. Dale, Feb 06 2015 *)

PROG

(Magma) [ n: n in [0..50000] | not 0 in Intseq(2^n) ]; // Bruno Berselli, Jun 08 2011

(Perl) use bignum;

for(0..99) {

if((1<<$_) =~ /^[1-9]+$/) {

print "$_, "

}

(PARI) for(n=0, 99, if(vecmin(eval(Vec(Str(2^n)))), print1(n", "))) \\ Charles R Greathouse IV, Jun 30 2011

(Haskell)

import Data.List (elemIndices)

a007377 n = a007377_list !! (n-1)

a007377_list = elemIndices 0 a027870_list

(Python)

def ok(n): return '0' not in str(2**n)

CROSSREFS

Some similar sequences are listed in A035064.