A113157 - OEIS

A113157

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

283, 409, 739, 983, 1021, 2213, 2251, 2339, 2663, 2749, 3079, 3821, 3931, 4219, 4463, 4799, 4919, 5413, 5741, 6271, 6917, 7703, 7753, 7873, 8287, 8861, 9013, 10091, 10427, 10709, 11317, 11483, 12421, 12917, 13037, 13693, 13781, 14029, 14759

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OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..39.

FORMULA

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.

EXAMPLE

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

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

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

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

MATHEMATICA

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

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

CROSSREFS