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A112795
Primes such that the sum of the predecessor and successor primes is divisible by 13.
15
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
OFFSET
1,1
COMMENTS
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.
LINKS
FORMULA
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.
EXAMPLE
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.
MATHEMATICA
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 *)
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 01 2006
EXTENSIONS
More terms from Robert G. Wilson v, Jan 05 2006
STATUS
approved