

A007377


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


52



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
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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
R. G. Wilson, V, Letter to N. J. A. Sloane, Oct. 1993


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<<$_) =~ /^[19]+$/) {
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 !! (n1)
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 * A305932 A213882 A135140
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



