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Search: id:A112804
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| A112804 |
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Primes such that the sum of the predecessor and successor primes is divisible by 19. |
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+0
15
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| 59, 97, 683, 797, 821, 1049, 1307, 1579, 1709, 1787, 1913, 2029, 2143, 2161, 2281, 2339, 2393, 2437, 2557, 2659, 2791, 2851, 2887, 3389, 3413, 3533, 3557, 3643, 3779, 3853, 4177, 4241, 4447, 4507, 4583, 4957, 4973, 5119, 5641, 5813, 6043, 6133, 7069
(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 19. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 19.
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EXAMPLE
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a(1) = 59 because prevprime(59) + nextprime(59) = 53 + 61 = 114 = 19 * 6.
a(2) = 97 because prevprime(97) + nextprime(97) = 89 + 101 = 190 = 19 * 10.
a(3) = 683 because prevprime(683) + nextprime(683) = 677 + 691 = 1368 = 19 * 72.
a(4) = 797 because prevprime(797) + nextprime(797) = 787 + 809 = 1596 = 19 * 84.
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MATHEMATICA
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Prime@ Select[Range[2, 912], Mod[Prime[ # - 1] + Prime[ # + 1], 19] == 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: A112801 A112802 A112803 this_sequence A112805 A112806 A112807
Sequence in context: A039431 A043254 A044034 this_sequence A134573 A106869 A060259
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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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