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

1,2

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

Prog

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

Crossrefs

Cf. A037053.

Sequence in context: A371968 A335467 A256474 * A351290 A244511 A014157

Adjacent sequences: A085821 A085822 A085823 * A085825 A085826 A085827

Keyword

nonn,base

Author

Robert G. Wilson v, Jul 04 2003

Extensions

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

Status

approved