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A305947
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Number of powers of 7 having exactly n digits '0' (in base 10), conjectured.
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9
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10, 11, 12, 13, 9, 10, 9, 7, 10, 14, 21, 10, 18, 7, 11, 11, 12, 15, 17, 10, 11, 6, 10, 16, 13, 9, 7, 9, 11, 12, 10, 16, 7, 16, 9, 14, 13, 13, 9, 17, 14, 12, 11, 9, 13, 9, 12, 12, 9, 12, 14
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OFFSET
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0,1
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COMMENTS
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a(0) = 10 is the number of terms in A030703 and in A195908, which includes the power 7^0 = 1.
These are the row lengths of A305927. It remains an open problem to provide a proof that these rows are complete (as for all terms of A020665), but the search has been pushed to many orders of magnitude beyond the largest known term, and the probability of finding an additional term is vanishing, cf. Khovanova link.
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LINKS
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Table of n, a(n) for n=0..50.
M. F. Hasler, Zeroless powers, OEIS Wiki, March 2014, updated 2018.
T. Khovanova, The 86-conjecture, Tanya Khovanova's Math Blog, Feb. 2011.
W. Schneider, No Zeros, 2000, updated 2003. (On web.archive.org--see A007496 for a cached copy.)
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PROG
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(PARI) A305947(n, M=99*n+199)=sum(k=0, M, #select(d->!d, digits(7^k))==n)
(PARI) A305947_vec(nMax, M=99*nMax+199, a=vector(nMax+=2))={for(k=0, M, a[min(1+#select(d->!d, digits(7^k)), nMax)]++); a[^-1]}
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CROSSREFS
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Cf. A030703 (= row 0 of A305927): k such that 7^k has no 0's; A195908: these powers 7^k.
Cf. A020665: largest k such that n^k has no '0's.
Cf. A063606 (= column 1 of A305927): least k such that 7^k has n digits '0' in base 10.
Cf. A305942 (analog for 2^k), ..., A305946, A305938, A305939 (analog for 9^k).
Sequence in context: A303657 A342367 A303879 * A100830 A180176 A350494
Adjacent sequences: A305944 A305945 A305946 * A305948 A305949 A305950
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KEYWORD
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nonn,base
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AUTHOR
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M. F. Hasler, Jun 22 2018
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STATUS
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approved
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