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A157772
Numbers n such that 100n + 13 is prime.
7
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, ...
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
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