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

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

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

Sequence in context: A142937 A081424 A142699 * A142446 A345905 A059257

Adjacent sequences: A113154 A113155 A113156 * A113158 A113159 A113160

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 05 2006

Extensions

More terms from Robert G. Wilson v, Jan 11 2006

Status

approved