A112804 Primes such that the sum of the predecessor and successor primes is divisible by 19.

59, 97, 683, 797, 821, 1049, 1307, 1579, 1709, 1787, 1913, 2029, 2143, 2161, 2281, 2339, 2393, 2437, 2557, 2659, 2791, 2851, 2887, 3389, 3413, 3533, 3557, 3643, 3779, 3853, 4177, 4241, 4447, 4507, 4583, 4957, 4973, 5119, 5641, 5813, 6043, 6133, 7069

Offset: 1

Author

Jonathan Vos Post, Jan 01 2006

Keywords

• easy
• nonn

Comments

There is a trivial analog for every prime >= 3. A112681 is analogous mod 3. A112731 is analogous mod 7. A112789 is analogous mod 11.

Examples

			a(1) = 59 because prevprime(59) + nextprime(59) = 53 + 61 = 114 = 19 * 6.
a(2) = 97 because prevprime(97) + nextprime(97) = 89 + 101 = 190 = 19 * 10.
a(3) = 683 because prevprime(683) + nextprime(683) = 677 + 691 = 1368 = 19 * 72.
a(4) = 797 because prevprime(797) + nextprime(797) = 787 + 809 = 1596 = 19 * 84.
		

Crossrefs

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

Mathematica

Prime@ Select[Range[2, 912], Mod[Prime[ # - 1] + Prime[ # + 1], 19] == 0 &] (* Robert G. Wilson v *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 19. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 19.

Extensions

More terms from Robert G. Wilson v, Jan 05 2006