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A306112 Largest k such that 2^k has exactly n digits 0 (in base 10), conjectured.

%I A306112 #5 Jun 23 2018 09:19:26
%S A306112 86,229,231,359,283,357,475,476,649,733,648,696,824,634,732,890,895,
%T A306112 848,823,929,1092,1091,1239,1201,1224,1210,1141,1339,1240,1282,1395,
%U A306112 1449,1416,1408,1616,1524,1727,1725,1553,1942,1907,1945,1870,1724,1972,1965,2075,1983,2114,2257,2256
%N A306112 Largest k such that 2^k has exactly n digits 0 (in base 10), conjectured.
%C A306112 a(0) is the largest term in A007377: exponents of powers of 2 without digit 0.
%C A306112 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 A306112 M. F. Hasler, <a href="/wiki/Zeroless_Powers">Zeroless powers</a>, OEIS Wiki, March 2014, updated 2018.
%H A306112 T. Khovanova, <a href="https://blog.tanyakhovanova.com/2011/02/86-conjecture/">The 86-conjecture</a>, Tanya Khovanova's Math Blog, Feb. 2011.
%H A306112 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 A306112 (PARI) A306112_vec(nMax,M=99*nMax+199,x=2,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}
%Y A306112 Cf. A031146: least k such that 2^k has n digits 0 in base 10.
%Y A306112 Cf. A305942: number of k's such that 2^k has n digits 0.
%Y A306112 Cf. A305932: row n lists exponents of 2^k with n digits 0.
%Y A306112 Cf. A007377: { k | 2^k has no digit 0 } : row 0 of the above.
%Y A306112 Cf. A238938: { 2^k having no digit 0 }.
%Y A306112 Cf. A027870: number of 0's in 2^n (and A065712, A065710, A065714, A065715, A065716, A065717, A065718, A065719, A065744 for digits 1 .. 9).
%Y A306112 Cf. A102483: 2^n contains no 0 in base 3.
%K A306112 nonn,base
%O A306112 0,1
%A A306112 _M. F. Hasler_, Jun 22 2018