cp's OEIS Frontend

A306114 Largest k such that 4^k has exactly n digits 0 (in base 10), conjectured.

%I A306114 #6 Jun 23 2018 14:19:00
%S A306114 43,92,77,88,115,171,182,238,235,308,324,348,412,317,366,445,320,424,
%T A306114 362,448,546,423,540,545,612,605,567,571,620,641,619,700,708,704,808,
%U A306114 762,811,744,755,971,896,900,935,862,986,954,982,956,1057,1037,1128
%N A306114 Largest k such that 4^k has exactly n digits 0 (in base 10), conjectured.
%C A306114 a(0) is the largest term in A030701: exponents of powers of 4 without digit 0 in base 10.
%C A306114 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 A306114 M. F. Hasler, <a href="/wiki/Zeroless_Powers">Zeroless powers</a>, OEIS Wiki, March 2014, updated 2018.
%H A306114 T. Khovanova, <a href="https://blog.tanyakhovanova.com/2011/02/86-conjecture/">The 86-conjecture</a>, Tanya Khovanova's Math Blog, Feb. 2011.
%H A306114 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 A306114 (PARI) A306114_vec(nMax,M=99*nMax+199,x=4,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}
%Y A306114 Cf. A063575: least k such that 4^k has n digits 0 in base 10.
%Y A306114 Cf. A305944: number of k's such that 4^k has n digits 0.
%Y A306114 Cf. A305924: row n lists exponents of 4^k with n digits 0.
%Y A306114 Cf. A030701: { k | 4^k has no digit 0 } : row 0 of the above.
%Y A306114 Cf. A238940: { 4^k having no digit 0 }.
%Y A306114 Cf. A020665: largest k such that n^k has no digit 0 in base 10.
%Y A306114 Cf. A071531: least k such that n^k contains a digit 0 in base 10.
%Y A306114 Cf. A103663: least x such that x^n has no digit 0 in base 10.
%Y A306114 Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.
%K A306114 nonn,base
%O A306114 0,1
%A A306114 _M. F. Hasler_, Jun 22 2018