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A112795
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Primes such that the sum of the predecessor and successor primes is divisible by 13.
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15
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79, 103, 139, 233, 271, 389, 401, 457, 587, 619, 641, 769, 883, 967, 1013, 1031, 1153, 1213, 1249, 1289, 1301, 1429, 1523, 1559, 1571, 1699, 1721, 1789, 1847, 1901, 2039, 2089, 2111, 2273, 2297, 2459, 2579, 2593, 2663, 3359, 3371, 3373, 3449, 3491, 3527
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OFFSET
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1,1
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COMMENTS
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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. A112789 is analogous to this, but mod 11.
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LINKS
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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 13. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 13.
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EXAMPLE
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a(1) = 79 because prevprime(79) + nextprime(79) = 73 + 83 = 156 = 13 * 12.
a(2) = 103 because prevprime(103) + nextprime(103) = 101 + 107 = 208 = 13 * 16.
a(3) = 139 because prevprime(139) + nextprime(139) = 137 + 149 = 286 = 13 * 22.
a(4) = 233 because prevprime(233) + nextprime(233) = 229 + 239 = 468 = 13 * 36.
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MATHEMATICA
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Prime@ Select[Range[2, 496], Mod[Prime[ # - 1] + Prime[ # + 1], 13] == 0 &] (* Robert G. Wilson v *)
Select[Partition[Prime[Range[500]], 3, 1], Divisible[#[[1]]+#[[3]], 13]&] [[All, 2]] (* Harvey P. Dale, Apr 06 2022 *)
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CROSSREFS
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Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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