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A306113 Largest k such that 3^k has exactly n digits 0 (in base 10), conjectured.

%I A306113 #8 Jun 23 2018 10:15:19
%S A306113 68,73,136,129,205,237,317,268,251,276,343,372,389,419,565,416,494,
%T A306113 571,637,628,713,629,638,655,735,690,862,802,750,863,826,996,976,1008,
%U A306113 1085,1026,1130,995,962,1082,1136,1064,1176,1084,1215,1354,1298,1275,1226,1468,1353
%N A306113 Largest k such that 3^k has exactly n digits 0 (in base 10), conjectured.
%C A306113 a(0) is the largest term in A030700: exponents of powers of 3 without digit 0.
%C A306113 There is no proof for any of the terms, just as for any term of A020665 and many similar / related sequences. However, the search has been pushed to many magnitudes beyond the largest known term, and the probability of any of the terms being wrong is extremely small, cf., e.g., the Khovanova link.
%H A306113 M. F. Hasler, <a href="/wiki/Zeroless_Powers">Zeroless powers</a>, OEIS Wiki, March 2014, updated 2018.
%H A306113 T. Khovanova, <a href="https://blog.tanyakhovanova.com/2011/02/86-conjecture/">The 86-conjecture</a>, Tanya Khovanova's Math Blog, Feb. 2011.
%H A306113 W. Schneider, <a href="http://web.archive.org/web/20050407120908/http://www.wschnei.de:80/digit-related-numbers/nozeros.html">No Zeros</a>, 2000, updated 2003. (On web.archive.org--see A007496 for a cached copy.)
%o A306113 (PARI) A306113_vec(nMax,M=99*nMax+199,x=3,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}
%Y A306113 Cf. A063555: least k such that 3^k has n digits 0 in base 10.
%Y A306113 Cf. A305943: number of k's such that 3^k has n digits 0.
%Y A306113 Cf. A305933: row n lists exponents of 3^k with n digits 0.
%Y A306113 Cf. A030700: { k | 3^k has no digit 0 } : row 0 of the above.
%Y A306113 Cf. A238939: { 3^k having no digit 0 }.
%Y A306113 Cf. A305930: number of 0's in 3^n.
%Y A306113 Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.
%K A306113 nonn,base
%O A306113 0,1
%A A306113 _M. F. Hasler_, Jun 22 2018