A113157 - OEIS

%I #8 Oct 31 2013 12:17:34

%S 283,409,739,983,1021,2213,2251,2339,2663,2749,3079,3821,3931,4219,

%T 4463,4799,4919,5413,5741,6271,6917,7703,7753,7873,8287,8861,9013,

%U 10091,10427,10709,11317,11483,12421,12917,13037,13693,13781,14029,14759

%N Primes such that the sum of the predecessor and successor primes is divisible by 41.

%C A112681 is mod 3 analogy. A112794 is mod 5 analogy. A112731 is mod 7 analogy. A112789 is mod 11 analogy. A112795 is mod 13 analogy. A112796 is mod 17 analogy. A112804 is mod 19 analogy. A112847 is mod 23 analogy. A112859 is mod 29 analogy.

%F a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 41. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 41.

%e a(1) = 283 since prevprime(283) + nextprime(283) = 281 + 293 = 574 = 41 * 14.

%e a(2) = 409 since prevprime(409) + nextprime(409) = 401 + 419 = 820 = 41 * 20.

%e a(3) = 739 since prevprime(739) + nextprime(739) = 733 + 743 = 1476 = 41 * 36.

%e a(4) = 983 since prevprime(983) + nextprime(983) = 977 + 991 = 1968 = 41 * 48.

%t Prime@Select[Range[2, 1766], Mod[Prime[ # - 1] + Prime[ # + 1], 41] == 0 &] (* _Robert G. Wilson v_ *)

%t Transpose[Select[Partition[Prime[Range[2000]],3,1],Divisible[First[#] + Last[#], 41]&]][[2]] (* _Harvey P. Dale_, Jul 25 2012 *)

%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 05 2006

%E More terms from _Robert G. Wilson v_, Jan 11 2006