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A007377
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Numbers k such that the decimal expansion of 2^k contains no 0.
(Formerly M0485)
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55
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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)
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OFFSET
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1,3
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COMMENTS
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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^k, which seems to end with k=68. - M. F. Hasler, Mar 07 2014
Checked up to k = 10^10. - David Radcliffe, Dec 29 2015
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REFERENCES
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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).
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LINKS
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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
R. G. Wilson, V, Letter to N. J. A. Sloane, Oct. 1993
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MAPLE
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remove(t -> has(convert(2^t, base, 10), 0), [$0..1000]); # Robert Israel, Dec 29 2015
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MATHEMATICA
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Do[ If[ Union[ RealDigits[ 2^n ] [[1]]] [[1]] != 0, Print[ n ] ], {n, 1, 60000}]
Select[Range@1000, First@Union@IntegerDigits[2^# ] != 0 &]
Select[Range[0, 100], DigitCount[2^#, 10, 0]==0&] (* Harvey P. Dale, Feb 06 2015 *)
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PROG
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(MAGMA) [ n: n in [0..50000] | not 0 in Intseq(2^n) ]; // Bruno Berselli, Jun 08 2011
(Perl) use bignum;
for(0..99) {
if((1<<$_) =~ /^[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
(Python)
def ok(n): return '0' not in str(2**n)
print(list(filter(ok, range(10**4)))) # Michael S. Branicky, Aug 08 2021
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CROSSREFS
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Cf. A027870, A030700, A102483.
Cf. similar sequences listed in A035064.
Cf. A031142.
Sequence in context: A174887 A092598 A247811 * A305932 A213882 A135140
Adjacent sequences: A007374 A007375 A007376 * A007378 A007379 A007380
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KEYWORD
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base,nonn
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v
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EXTENSIONS
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a(1) = 0 prepended by Reinhard Zumkeller, Apr 30 2013
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STATUS
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approved
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