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A306117 Largest k such that 7^k has exactly n digits 0 (in base 10), conjectured.

%I A306117 #5 Jun 23 2018 14:19:38
%S A306117 35,51,93,58,122,74,108,131,118,152,195,192,236,184,247,243,254,286,
%T A306117 325,292,318,336,375,393,339,431,327,433,485,447,456,455,448,492,452,
%U A306117 507,489,541,526,605,627,706,730,628,665,660,798,715,704,633,728
%N A306117 Largest k such that 7^k has exactly n digits 0 (in base 10), conjectured.
%C A306117 a(0) is the largest term in A030703: exponents of powers of 7 without digit 0 in base 10.
%C A306117 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 A306117 M. F. Hasler, <a href="/wiki/Zeroless_Powers">Zeroless powers</a>, OEIS Wiki, March 2014, updated 2018.
%H A306117 T. Khovanova, <a href="https://blog.tanyakhovanova.com/2011/02/86-conjecture/">The 86-conjecture</a>, Tanya Khovanova's Math Blog, Feb. 2011.
%H A306117 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 A306117 (PARI) A306117_vec(nMax,M=99*nMax+199,x=7,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}
%Y A306117 Cf. A063606: least k such that 7^k has n digits 0 in base 10.
%Y A306117 Cf. A305947: number of k's such that 7^k has n digits 0.
%Y A306117 Cf. A305927: row n lists exponents of 6^k with n digits 0.
%Y A306117 Cf. A030703: { k | 7^k has no digit 0 } : row 0 of the above.
%Y A306117 Cf. A195908: { 7^k having no digit 0 }.
%Y A306117 Cf. A020665: largest k such that n^k has no digit 0 in base 10.
%Y A306117 Cf. A071531: least k such that n^k contains a digit 0 in base 10.
%Y A306117 Cf. A103663: least x such that x^n has no digit 0 in base 10.
%Y A306117 Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.
%K A306117 nonn,base
%O A306117 0,1
%A A306117 _M. F. Hasler_, Jun 22 2018