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Search: id:A112847
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| A112847 |
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Primes such that the sum of the predecessor and successor primes is divisible by 23. |
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+0
15
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| 229, 277, 317, 461, 643, 919, 1033, 1307, 1427, 1609, 1777, 1789, 2089, 2207, 2347, 2531, 2551, 2647, 2969, 3121, 3169, 3517, 3659, 3701, 3727, 4211, 4421, 4549, 4903, 5039, 5309, 5431, 5867, 5881, 6091, 6211, 6277, 6673, 6781, 6803, 7309, 7499, 8147
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 23. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 23.
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EXAMPLE
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a(1) = 229 because prevprime(229) + nextprime(229) = 227 + 433 = 460 = 23 * 20.
a(2) = 277 because prevprime(277) + nextprime(277) = 271 + 281 = 552 = 23 * 24.
a(3) = 317 because prevprime(317) + nextprime(317) = 313 + 331 = 644 = 23 * 28.
a(4) = 461 because prevprime(461) + nextprime(461) = 457 + 463 = 920 = 23 * 40.
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MATHEMATICA
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Prime@ Select[Range[2, 1032], Mod[Prime[ # - 1] + Prime[ # + 1], 23] == 0 &] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.
Adjacent sequences: A112844 A112845 A112846 this_sequence A112848 A112849 A112850
Sequence in context: A119711 A062589 A094612 this_sequence A139512 A124684 A028452
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 01 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 05 2006
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