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Powers of 11 which have no zero in their decimal expansion.
23

%I #23 Jan 28 2023 14:01:08

%S 1,11,121,1331,14641,1771561,19487171,214358881,2357947691,

%T 3138428376721,34522712143931,379749833583241,4177248169415651,

%U 45949729863572161,5559917313492231481,4978518112499354698647829163838661251242411

%N Powers of 11 which have no zero in their decimal expansion.

%C Probably finite. Is 4978518112499354698647829163838661251242411 the largest term?

%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 a(n) = 11^A030706(n).

%F A195946 = A001020 intersect A052382.

%t Select[11^Range[0,50],DigitCount[#,10,0]==0&] (* _Harvey P. Dale_, Jan 27 2014 *)

%o (PARI) for( n=0,9999, is_A052382(11^n) && print1(11^n,","))

%o (Magma) [11^n: n in [0..3*10^4] | not 0 in Intseq(11^n)]; // _Bruno Berselli_, Sep 26 2011

%Y For the zeroless numbers (powers x^n), see A195942, A195943, A238938, A238939, A238940, A195948, A238936, A195908, A195945.

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

%K nonn,base

%O 1,2

%A _M. F. Hasler_, Sep 25 2011

%E Keyword:fini removed by _Jianing Song_, Jan 28 2023 as finiteness is only conjectured.