cp's OEIS Frontend

A306118 Largest k such that 8^k has exactly n digits 0 (in base 10), conjectured.

%I A306118 #9 Dec 21 2024 23:15:12
%S A306118 27,43,77,61,69,119,115,158,159,168,216,232,202,198,244,270,229,274,
%T A306118 241,273,364,283,413,298,408,341,378,431,404,403,465,483,472,454,467,
%U A306118 508,540,575,485,576,511,623,538,515,560,655,647,661,648,639,752
%N A306118 Largest k such that 8^k has exactly n digits 0 (in base 10), conjectured.
%C A306118 a(0) is the largest term in A030704: exponents of powers of 8 without digit 0 in base 10.
%C A306118 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 A306118 M. F. Hasler, <a href="https://oeis.org/wiki/Zeroless_powers">Zeroless powers</a>, OEIS Wiki, Mar 07 2014, updated 2018.
%H A306118 T. Khovanova, <a href="https://blog.tanyakhovanova.com/2011/02/86-conjecture/">The 86-conjecture</a>, Tanya Khovanova's Math Blog, Feb. 2011.
%H A306118 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 A306118 (PARI) A306118_vec(nMax,M=99*nMax+199,x=8,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}
%Y A306118 Cf. A063616: least k such that 8^k has n digits 0 in base 10.
%Y A306118 Cf. A305938: number of k's such that 8^k has n digits 0.
%Y A306118 Cf. A305928: row n lists exponents of 8^k with n digits 0.
%Y A306118 Cf. A030704: { k | 8^k has no digit 0 } : row 0 of the above.
%Y A306118 Cf. A020665: largest k such that n^k has no digit 0 in base 10.
%Y A306118 Cf. A071531: least k such that n^k contains a digit 0 in base 10.
%Y A306118 Cf. A103663: least x such that x^n has no digit 0 in base 10.
%Y A306118 Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.
%K A306118 nonn,base
%O A306118 0,1
%A A306118 _M. F. Hasler_, Jun 22 2018