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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 (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^k, which seems to end with k=68. - M. F. Hasler, Mar 07 2014
Checked up to k = 10^10. - David Radcliffe, Aug 21 2022
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
W. Schneider, NoZeros: Powers n^k without Digit Zero [Cached copy]
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]+$/) {
print "$_, "
}
} # 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
CROSSREFS
Some similar sequences are listed in A035064.
Cf. also A031142.
Sequence in context: A174887 A092598 A247811 * A305932 A213882 A135140
KEYWORD
base,nonn
AUTHOR
EXTENSIONS
a(1) = 0 prepended by Reinhard Zumkeller, Apr 30 2013
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)