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A007377 Numbers n such that the decimal expansion of 2^n contains no 0.
(Formerly M0485)
46
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

A027870(a(n)) = A224782(a(n)) = 0. - Reinhard Zumkeller, Apr 30 2013

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

Checked up to n = 10^10. - David Radcliffe, Dec 29 2015

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

Table of n, a(n) for n=1..36.

David Radcliffe, Python script to search for powers with no zero digits

W. Schneider, NoZeros: Powers n^k without Digit Zero [Cached copy]

Eric Weisstein's World of Mathematics, Zero

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 "$_, "

  }

} # Charles R Greathouse IV, Jun 30 2011

(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

-- Reinhard Zumkeller, Apr 30 2013

CROSSREFS

Cf. A027870, A030700, A102483.

Cf. similar sequences listed in A035064.

Sequence in context: A174887 A092598 A247811 * A213882 A135140 A052061

Adjacent sequences:  A007374 A007375 A007376 * A007378 A007379 A007380

KEYWORD

base,nonn

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

EXTENSIONS

a(1) = 0 prepended by Reinhard Zumkeller, Apr 30 2013

STATUS

approved

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Last modified June 30 15:21 EDT 2016. Contains 274311 sequences.