A088262 -id:A088262 - cp's OEIS frontend

A088263 Diagonal of A088262.

11, 13, 37, 79, 911, 1213, 2417, 1619, 2521, 1823, 3727, 3329, 2731, 3833, 4637, 4339, 5741, 5843, 5347, 6949, 5651, 6353, 5657, 7459, 8461, 8363, 8467, 9769, 10771, 9173, 10177, 10979, 11681, 11483, 11087, 11789, 12391, 13093, 12697, 13499, 182101

Offset: 1

Amarnath Murthy, Sep 28 2003

Cf. A088262.

More terms from David Wasserman, Jul 27 2005

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

Original entry on oeis.org

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

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

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, ...

			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).

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

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

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

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

A110406 List of k primes ending in k, where k == 1, 3, 7 or 9 (mod 10).

Original entry on oeis.org

11, 3, 13, 23, 7, 17, 37, 47, 67, 97, 107, 19, 29, 59, 79, 89, 109, 139, 149, 179, 11, 211, 311, 811, 911, 1511, 1811, 2011, 2111, 2311, 2411, 13, 113, 313, 613, 1013, 1213, 1613, 1913, 2113, 2213, 2713, 3313, 3413, 17, 317, 617, 1117, 1217, 2017, 2417, 2617

Offset: 1

Amarnath Murthy, Jul 30 2005

Lists the 1st entry in A030430, the first 3 entries of A030431, the first 7 entries of A030432, the first 9 entries of A030433, the first 11 entries of A167442 etc.

			Terms corresponding to 7 are 7, 17, 37, 47, 67, 97, 127. 13 occurs for 3 as well as for 13.
11;
3,13,23;
7,17,37,47,67,97,107;
19,29,59,79,89,109,139,149,179;

Cf. A089779, A088262.

f[n_] := Take[ Select[p, Mod[ #, 10^Floor[ Log[10, n] + 1]] == n &], n]; p = Prime[ Range[10^5]]; lst = Select[ Range[1, 17, 2], Mod[ #, 10] != 5 &] (* Robert G. Wilson v *)

Corrected and extended by Robert G. Wilson v, Jul 30 2005

cp's OEIS Frontend

A088263 Diagonal of A088262.

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

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PARI

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A110406 List of k primes ending in k, where k == 1, 3, 7 or 9 (mod 10).

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Mathematica

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