A112804 - OEIS

%I #7 Oct 31 2013 12:17:34

%S 59,97,683,797,821,1049,1307,1579,1709,1787,1913,2029,2143,2161,2281,

%T 2339,2393,2437,2557,2659,2791,2851,2887,3389,3413,3533,3557,3643,

%U 3779,3853,4177,4241,4447,4507,4583,4957,4973,5119,5641,5813,6043,6133,7069

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

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

%F 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.

%e a(1) = 59 because prevprime(59) + nextprime(59) = 53 + 61 = 114 = 19 * 6.

%e a(2) = 97 because prevprime(97) + nextprime(97) = 89 + 101 = 190 = 19 * 10.

%e a(3) = 683 because prevprime(683) + nextprime(683) = 677 + 691 = 1368 = 19 * 72.

%e a(4) = 797 because prevprime(797) + nextprime(797) = 787 + 809 = 1596 = 19 * 84.

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

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

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Jan 01 2006

%E More terms from _Robert G. Wilson v_, Jan 05 2006