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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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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
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OFFSET
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1,1
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COMMENTS
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There is a trivial analog for every prime >= 3. A112681 is analogous mod 3. A112731 is analogous mod 7. A112789 is analogous mod 11.
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LINKS
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Table of n, a(n) for n=1..43.
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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.
Sequence in context: A043254 A044034 A142152 * A199977 A134573 A106869
Adjacent sequences: A112801 A112802 A112803 * A112805 A112806 A112807
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Jan 01 2006
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EXTENSIONS
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More terms from Robert G. Wilson v, Jan 05 2006
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STATUS
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approved
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