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

Author

Jonathan Vos Post, Dec 31 2005

Keywords

• easy
• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

Extensions

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