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

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

Offset: 1

Author

M. F. Hasler, Sep 25 2011

Keywords

• nonn
• base

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

• 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 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.

Programs

Magma

[13^n: n in [0..2*10^4] | not 0 in Intseq(13^n)]; // Bruno Berselli, Sep 26 2011

Mathematica

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

PARI

for(n=0,9999, is_A052382(13^n) && print1(13^n,","))

Formula

Equals A001022 intersect A052382 (as a set).

Equals A001022 o A195944 (as a function).