A195946 Powers of 11 which have no zero in their decimal expansion.

1, 11, 121, 1331, 14641, 1771561, 19487171, 214358881, 2357947691, 3138428376721, 34522712143931, 379749833583241, 4177248169415651, 45949729863572161, 5559917313492231481, 4978518112499354698647829163838661251242411

Offset: 1

Author

M. F. Hasler, Sep 25 2011

Keywords

• nonn
• base

Comments

Probably finite. Is 4978518112499354698647829163838661251242411 the largest term?

Links

• M. F. Hasler, Zeroless powers, OEIS Wiki, Mar 07 2014
• C. Rivera, Puzzle 607. A zeroless Prime power, on primepuzzles.net, Sept. 24, 2011.
• W. Schneider, NoZeros: Powers n^k without Digit Zero (local copy of www.wschnei.de/digit-related-numbers/nozeros.html), as of Jan 30 2003.

Crossrefs

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

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

Programs

Magma

[11^n: n in [0..3*10^4] | not 0 in Intseq(11^n)]; // Bruno Berselli, Sep 26 2011

Mathematica

Select[11^Range[0,50],DigitCount[#,10,0]==0&] (* Harvey P. Dale, Jan 27 2014 *)

PARI

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

Formula

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

A195946 = A001020 intersect A052382.

Extensions

Keyword:fini removed by Jianing Song, Jan 28 2023 as finiteness is only conjectured.