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 A112731 Primes such that the sum of the predecessor and successor primes is divisible by 7. 15
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified February 7 10:30 EST 2023. Contains 360115 sequences. (Running on oeis4.)