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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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Table of n, a(n) for n=1..45.
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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 *)
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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: A193142 A033250 A139922 * A107162 A135143 A139503
Adjacent sequences: A112792 A112793 A112794 * A112796 A112797 A112798
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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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