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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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Sequence in context: A243531 A139505 A095745 * A186459 A020359 A185936

Adjacent sequences:  A112793 A112794 A112795 * A112797 A112798 A112799

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 June 18 01:16 EDT 2021. Contains 345098 sequences. (Running on oeis4.)