A195946 - OEIS

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

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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: A374725 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