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

1,1

Links

Table of n, a(n) for n=1..45.

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.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A139883 A060834 A060844 * A266989 A161615 A307950

Adjacent sequences: A112786 A112787 A112788 * A112790 A112791 A112792

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 01 2006

Extensions

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

Status

approved