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A112796
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Primes such that the sum of the predecessor and successor primes is divisible by 17.
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15
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151, 191, 199, 421, 491, 613, 829, 883, 937, 1409, 1447, 1459, 1667, 1693, 1871, 2027, 2203, 2347, 2381, 2503, 2687, 2857, 2957, 3041, 3121, 3259, 3517, 3557, 3571, 3583, 3847, 3929, 4153, 4271, 4591, 4793, 4999, 5011, 5051, 5273, 5323, 5407, 5441, 5449
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| There is a trivial analogy to every prime beyond 3, but mod 2. A112681 is analogous to this, but mod 3. A112731 is analogous to this, but mod 7. A112xxx is analogous to this, but mod 11.
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FORMULA
| a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 17. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 17.
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EXAMPLE
| a(1) = 151 because prevprime(151) + nextprime(151) = 149 + 157 = 306 = 17 * 8.
a(2) = 191 because prevprime(191) + nextprime(191) = 181 + 193 = 374 = 17 * 22.
a(3) = 199 because prevprime(199) + nextprime(199) = 197 + 211 = 408 = 17 * 24.
a(4) = 421 because prevprime(421) + nextprime(421) = 419 + 431 = 850 = 17 * 50.
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MATHEMATICA
| Prime@ Select[Range[2, 731], Mod[Prime[ # - 1] + Prime[ # + 1], 17] == 0 &] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.
Sequence in context: A180554 A139505 A095745 * A186459 A020359 A185936
Adjacent sequences: A112793 A112794 A112795 * A112797 A112798 A112799
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 01 2006
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 05 2006
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