A195945 Powers of 13 which have no zero in their decimal expansion.

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

Offset

1,2

Comments

Probably finite. Is 3937376385699289 the largest term?

No further terms up to 13^25000. - Harvey P. Dale, Oct 01 2011

No further terms up to 13^45000. - Vincenzo Librandi, Jul 31 2013

No further terms up to 13^(10^9). - Daniel Starodubtsev, Mar 22 2020

Links

Table of n, a(n) for n=1..9.

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

Equals A001022 intersect A052382 (as a set).

Equals A001022 o A195944 (as a function).

Mathematica

Select[13^Range[0, 250], DigitCount[#, 10, 0]==0&] (* Harvey P. Dale, Oct 01 2011 *)

Prog

(PARI) for(n=0, 9999, is_A052382(13^n) && print1(13^n, ", "))
(Magma) [13^n: n in [0..2*10^4] | not 0 in Intseq(13^n)]; // Bruno Berselli, Sep 26 2011

Crossrefs

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

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

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

Sequence in context: A045597 A045600 A001022 * A228389 A020533 A176596

Adjacent sequences: A195942 A195943 A195944 * A195946 A195947 A195948

Keyword

nonn,base

Author

M. F. Hasler, Sep 25 2011

Status

approved