A112789 Primes such that the sum of the predecessor and successor primes is divisible by 11.

31, 43, 67, 109, 131, 139, 191, 617, 727, 881, 911, 937, 953, 991, 1049, 1289, 1381, 1429, 1543, 1571, 1619, 1657, 1693, 1721, 1723, 1777, 1783, 1871, 1979, 2251, 2311, 2341, 2377, 2441, 2531, 2579, 2837, 2953, 3061, 3221, 3257, 3557, 3559, 3631, 3673

Offset: 1

Author

Jonathan Vos Post, Jan 01 2006

Keywords

• easy
• nonn

Examples

			a(1) = 31 because prevprime(31) + nextprime(31) = 29 + 37 = 66 = 11 * 6.
a(2) = 43 because prevprime(43) + nextprime(43) = 41 + 47 = 88 = 11 * 8.
a(3) = 67 because prevprime(67) + nextprime(67) = 61 + 71 = 132 = 11 * 12.
a(4) = 109 because prevprime(109) + nextprime(109) = 107 + 113 = 220 = 11 * 20.
		

Crossrefs

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

Programs

Mathematica

Prime@ Select[Range[2, 515], Mod[Prime[ # - 1] + Prime[ # + 1], 11] == 0 &] (* Robert G. Wilson v *)
Transpose[Select[Partition[Prime[Range[550]],3,1],Divisible[First[#]+ Last[#], 11]&]][[2]] (* Harvey P. Dale, Jul 22 2011 *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 11. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 11.

Extensions

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