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A112796
Primes such that the sum of the predecessor and successor primes is divisible by 17.
15
151, 191, 199, 421, 491, 613, 829, 883, 937, 1409, 1447, 1459, 1667, 1693, 1871, 2027, 2203, 2347, 2381, 2503, 2687, 2857, 2957, 3041, 3121, 3259, 3517, 3557, 3571, 3583, 3847, 3929, 4153, 4271, 4591, 4793, 4999, 5011, 5051, 5273, 5323, 5407, 5441, 5449
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 17. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 17.
EXAMPLE
a(1) = 151 because prevprime(151) + nextprime(151) = 149 + 157 = 306 = 17 * 8.
a(2) = 191 because prevprime(191) + nextprime(191) = 181 + 193 = 374 = 17 * 22.
a(3) = 199 because prevprime(199) + nextprime(199) = 197 + 211 = 408 = 17 * 24.
a(4) = 421 because prevprime(421) + nextprime(421) = 419 + 431 = 850 = 17 * 50.
MATHEMATICA
Prime@ Select[Range[2, 731], Mod[Prime[ # - 1] + Prime[ # + 1], 17] == 0 &] (* Robert G. Wilson v *)
Select[Partition[Prime[Range[800]], 3, 1], Divisible[#[[1]]+#[[3]], 17]&][[All, 2]] (* Harvey P. Dale, Oct 06 2020 *)
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 01 2006
EXTENSIONS
More terms from Robert G. Wilson v, Jan 05 2006
STATUS
approved