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A113155
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Primes such that the sum of the predecessor and successor primes is divisible by 31.
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15
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311, 401, 863, 907, 1117, 1213, 1237, 1399, 1427, 2333, 3299, 3533, 3821, 3967, 4243, 4493, 5273, 5779, 6199, 6521, 7069, 8219, 8369, 8623, 8741, 8837, 8929, 9277, 9613, 10139, 10601, 10631, 10939, 11621, 11779, 12197, 12241, 12343, 12401, 12457
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OFFSET
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1,1
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COMMENTS
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A112681 is mod 3 analogy. A112794 is mod 5 analogy. A112731 is mod 7 analogy. A112789 is mod 11 analogy. A112795 is mod 13 analogy. A112796 is mod 17 analogy. A112804 is mod 19 analogy. A112847 is mod 23 analogy. A112859 is mod 29 analogy.
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
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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 31. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 31.
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EXAMPLE
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a(1) = 311 since prevprime(311) + nextprime(311) = 307 + 313 = 620 = 31 * 20.
a(2) = 401 since prevprime(401) + nextprime(401) = 397 + 409 = 806 = 31 * 26.
a(3) = 863 since prevprime(863) + nextprime(863) = 859 + 877 = 1736 = 31 * 56.
a(4) = 907 since prevprime(907) + nextprime(907) = 887 + 911 = 1798 = 31 * 58.
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MATHEMATICA
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Prime@Select[Range[2, 1531], Mod[Prime[ # - 1] + Prime[ # + 1], 31] == 0 &] (* Robert G. Wilson v *)
Transpose[Select[Partition[Prime[Range[1500]], 3, 1], Divisible[#[[1]]+#[[3]], 31]&]][[2]] (* From Harvey P. Dale, Mar 23 2012 *)
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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: A142005 A059225 A157717 * A142626 A142950 A104718
Adjacent sequences: A113152 A113153 A113154 * A113156 A113157 A113158
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Jan 05 2006
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EXTENSIONS
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Corrected and extended by Robert G. Wilson v, Jan 11 2006
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STATUS
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approved
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