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

1,2

Comments

Probably finite. Is 4978518112499354698647829163838661251242411 the largest term?

Links

Table of n, a(n) for n=1..16.

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.

Formula

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

A195946 = A001020 intersect A052382.

Mathematica

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

Prog

(PARI) for( n=0, 9999, is_A052382(11^n) && print1(11^n, ", "))
(Magma) [11^n: n in [0..3*10^4] | not 0 in Intseq(11^n)]; // Bruno Berselli, Sep 26 2011

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.

Sequence in context: A001020 A325203 A055479 * A003590 A072051 A092846

Adjacent sequences: A195943 A195944 A195945 * A195947 A195948 A195949

Keyword

nonn,base

Author

M. F. Hasler, Sep 25 2011

Extensions

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

Status

approved