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

1,1

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.

Links

Table of n, a(n) for n=1..43.

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.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A043254 A044034 A142152 * A240339 A199977 A134573

Adjacent sequences: A112801 A112802 A112803 * A112805 A112806 A112807

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 01 2006

Extensions

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

Status

approved