A085824 Numbers n such that the smallest prime containing exactly n 0's (A037053) requires only two nonzero digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 34, 35, 36, 37, 38, 39, 41, 44, 45, 48, 51, 52, 54, 55, 56, 57, 59, 61, 64, 66, 68, 77, 80, 83, 85, 97, 99, 100, 102, 103, 104, 106, 109, 111, 112, 114, 119, 120, 122, 127, 128

Offset: 1

Author

Robert G. Wilson v, Jul 04 2003

Keywords

• nonn
• base

Comments

In the first one thousand primes containing exactly n zeros, 140 use just two digits. 1008 is in the sequence.

Although this sequence probably thins out like the primes, it is infinite.

For indices n listed here (and no others), A037053(n) = a*10^(n+1)+b with a in {1,...,9} and b in {1, 3, 7, 9}. The sequence of numbers *not* in this sequence is 13, 22, 29, 31, 32, 33, 40, 42, 43, ... - M. F. Hasler, Feb 19 2016

Links

• Hans Havermann, Table of n, a(n) for n = 1..310

Crossrefs

Cf. A037053.

Programs

PARI

is_A085824(n)=forstep(m=n=10^(n+1),9*n,n,nextprime(m)M. F. Hasler, Feb 19 2016

Extensions

Sequence rechecked (per request) and edited by Charles R Greathouse IV, Aug 03 2010