A157772 Numbers n such that 100n + 13 is prime.

0, 1, 3, 6, 10, 12, 16, 19, 21, 22, 27, 33, 34, 36, 40, 45, 48, 51, 54, 58, 61, 70, 72, 85, 87, 90, 94, 96, 103, 105, 106, 111, 112, 118, 121, 124, 126, 127, 133, 135, 136, 139, 147, 148, 150, 153, 154, 159, 177, 180, 183, 184, 187, 189, 190, 192, 198, 199, 201, 210, 213, 216

Offset

1,3

Comments

The sequence is infinite, because by Dirichlet's theorem there are infinitely many primes in the arithmetic sequence A*n+B (n=1,2,...) if A an B are relatively prime.

The sequence also has an infinite set of pairs a(k+1)=a(k)+1 (two consecutive naturals), but no set of three consecutive naturals (each third natural is divisible by 3)

No term of the sequence is of form 3k+2, because the sum of digits of 100*(3k+2)+13 is divisible by 3, violating the requirement of the definition.

Indices (as k-th prime) of the first members are 6, 30, 65, 112, 170, 198, 255, 293, 319, 330, 396, 466, 480, 505, 554, 612, 648, 684, 714, 763, 797, 902, 922, 1061, 1086, 1121, 1164, 1186, 1265, 1286, 1295, ...

Links

Table of n, a(n) for n=1..62.

Formula

{a(n): 100*a(n)+13 in A000040}.

Example

a(1)=0: 100*0+13=13 smallest prime which ends in 13, see A000040(6).
a(2)=1: 100*1+13=113 second prime which ends in 13, see A000040(30).

Prog

(PARI) isok(n) = isprime(100*n + 13) \\ Michel Marcus, Jul 22 2013

Crossrefs

Cf. A088262 (6th row). - R. J. Mathar, Apr 18 2009

Sequence in context: A032732 A187352 A310044 * A187684 A287176 A310045

Adjacent sequences: A157769 A157770 A157771 * A157773 A157774 A157775

Keyword

nonn,easy

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 06 2009

Extensions

Edited, 27 inserted by R. J. Mathar, Apr 18 2009

Status

approved