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A306116 Largest k such that 6^k has exactly n digits 0 (in base 10), conjectured.

%I A306116 #7 Jun 23 2018 14:19:14
%S A306116 44,59,63,82,98,134,108,123,199,189,192,200,275,282,267,307,298,296,
%T A306116 391,338,340,396,328,436,432,478,484,615,428,529,492,515,536,523,627,
%U A306116 665,559,592,637,560,654,674,590,653,728,791,753,781,812,783,788
%N A306116 Largest k such that 6^k has exactly n digits 0 (in base 10), conjectured.
%C A306116 a(0) is the largest term in A030702: exponents of powers of 6 without digit 0 in base 10.
%C A306116 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 A306116 M. F. Hasler, <a href="/wiki/Zeroless_Powers">Zeroless powers</a>, OEIS Wiki, March 2014, updated 2018.
%H A306116 T. Khovanova, <a href="https://blog.tanyakhovanova.com/2011/02/86-conjecture/">The 86-conjecture</a>, Tanya Khovanova's Math Blog, Feb. 2011.
%H A306116 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 A306116 (PARI) A306116_vec(nMax,M=99*nMax+199,x=6,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}
%Y A306116 Cf. A063596: least k such that 6^k has n digits 0 in base 10.
%Y A306116 Cf. A305946: number of k's such that 6^k has n digits 0.
%Y A306116 Cf. A305926: row n lists exponents of 6^k with n digits 0.
%Y A306116 Cf. A030702: { k | 6^k has no digit 0 } : row 0 of the above.
%Y A306116 Cf. A238936: { 6^k having no digit 0 }.
%Y A306116 Cf. A020665: largest k such that n^k has no digit 0 in base 10.
%Y A306116 Cf. A071531: least k such that n^k contains a digit 0 in base 10.
%Y A306116 Cf. A103663: least x such that x^n has no digit 0 in base 10.
%Y A306116 Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.
%K A306116 nonn,base
%O A306116 0,1
%A A306116 _M. F. Hasler_, Jun 22 2018