A112731 Primes such that the sum of the predecessor and successor primes is divisible by 7.

3, 13, 61, 71, 83, 167, 197, 241, 271, 281, 283, 317, 347, 349, 379, 431, 457, 499, 503, 569, 617, 631, 641, 643, 701, 757, 761, 797, 827, 829, 863, 1061, 1151, 1163, 1217, 1321, 1381, 1471, 1481, 1483, 1531, 1543, 1553, 1609, 1619, 1667, 1669, 1777, 1877

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(1) = 3 because previousprime(3) + nextprime(3) = 2 + 5 = 7.
a(2) = 13 because previousprime(13) + nextprime(13) = 11 + 17 = 28 = 7 * 4.
a(3) = 61 because previousprime(61) + nextprime(61) = 59 + 67 = 126 = 7 * 18.
a(4) = 71 because previousprime(71) + nextprime(71) = 67 + 73 = 140 = 7 * 20.

Mathematica

For[n = 2, n < 300, n++, If[(Prime[n - 1] + Prime[n + 1])/7 == Floor[(Prime[n - 1] + Prime[n + 1])/7], Print[Prime[n]]]] (* Stefan Steinerberger *)
Prime@Select[Range[2, 298], Mod[Prime[ # - 1] + Prime[ # + 1], 7] == 0 &] (* Robert G. Wilson v, Jan 11 2006 *)
Transpose[Select[Partition[Prime[Range[7000]], 3, 1], Divisible[First[#]+ Last[#], 7]&]][[2]] (* Harvey P. Dale, Jun 11 2013 *)

Crossrefs

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

Sequence in context: A340417 A292796 A020007 * A106884 A232611 A238445

Adjacent sequences: A112728 A112729 A112730 * A112732 A112733 A112734

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 31 2005

Extensions

More terms from Stefan Steinerberger and Robert G. Wilson v, Jan 02 2006

Status

approved