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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 (list; graph; refs; listen; history; text; internal format)
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 *)
CROSSREFS
Sequence in context: A243531 A139505 A095745 * A186459 A020359 A185936
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 01 2006
EXTENSIONS
More terms from Robert G. Wilson v, Jan 05 2006
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)