A195908 Powers of 7 which have no zero in their decimal expansion.

1, 7, 49, 343, 117649, 823543, 282475249, 1977326743, 11398895185373143, 378818692265664781682717625943

Offset: 1

Author

M. F. Hasler, Sep 25 2011

Keywords

• nonn
• base

Comments

Probably finite. Is 378818692265664781682717625943 the largest term?

No further terms up to 7^50,000, a number with 42,255 digits. - Harvey P. Dale, Jul 14 2022

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

Cf. A195942, A195943, A195944, A195945, A195946, A195948, A007377, A008839, A030700, A030701, A030702, A030703, A030704, A030705, A030706.

Programs

Magma

[7^n: n in [0..3*10^4] | not 0 in Intseq(7^n)]; // Bruno Berselli, Sep 26 2011

Mathematica

Select[7^Range[0,50],DigitCount[#,10,0]==0&] (* Harvey P. Dale, Jul 14 2022 *)

PARI

for( n=1,9999, is_A052382(7^n) && print1(7^n,","))

Formula

a(n) = 7^A030703(n).

A000420 intersect A052382.

Extensions

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