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A112731
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Primes such that the sum of the predecessor and successor primes is divisible by 7.
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15
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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; internal format)
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OFFSET
| 1,1
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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.
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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]]]] (Steinerberger)
Prime@Select[Range[2, 298], Mod[Prime[ # - 1] + Prime[ # + 1], 7] == 0 &] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 11 2006)
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CROSSREFS
| Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.
Sequence in context: A026578 A199641 A020007 * A106884 A112568 A104089
Adjacent sequences: A112728 A112729 A112730 * A112732 A112733 A112734
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 31 2005
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Robert G. Wilson v (rgwv(at)rgwv.com), Jan 02 2006
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