%I #32 Sep 08 2022 08:45:59

%S 1,13,169,2197,28561,371293,62748517,137858491849,3937376385699289

%N Powers of 13 which have no zero in their decimal expansion.

%C Probably finite. Is 3937376385699289 the largest term?

%C No further terms up to 13^25000. - _Harvey P. Dale_, Oct 01 2011

%C No further terms up to 13^45000. - _Vincenzo Librandi_, Jul 31 2013

%C No further terms up to 13^(10^9). - _Daniel Starodubtsev_, Mar 22 2020

%H M. F. Hasler, <a href="https://oeis.org/wiki/Zeroless_powers">Zeroless powers</a>, OEIS Wiki, Mar 07 2014

%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_607.htm">Puzzle 607. A zeroless Prime power</a>, on primepuzzles.net, Sept. 24, 2011.

%H W. Schneider, <a href="http://oeis.org/A007496/a007496.html">NoZeros: Powers n^k without Digit Zero</a> (local copy of www.wschnei.de/digit-related-numbers/nozeros.html), as of Jan 30 2003.

%F Equals A001022 intersect A052382 (as a set).

%F Equals A001022 o A195944 (as a function).

%t Select[13^Range[0,250],DigitCount[#,10,0]==0&] (* _Harvey P. Dale_, Oct 01 2011 *)

%o (PARI) for(n=0,9999, is_A052382(13^n) && print1(13^n,","))

%o (Magma) [13^n: n in [0..2*10^4] | not 0 in Intseq(13^n)]; // _Bruno Berselli_, Sep 26 2011

%Y For other zeroless powers x^n, see A238938 (x=2), A238939, A238940, A195948, A238936, A195908, A195946 (x=11), A195945, A195942, A195943, A103662.

%Y For the corresponding exponents, see A007377, A008839, A030700, A030701, A008839, A030702, A030703, A030704, A030705, A030706, A195944 and also A020665.

%Y For other related sequences, see A052382, A027870, A102483, A103663.

%K nonn,base

%O 1,2

%A _M. F. Hasler_, Sep 25 2011