A112859 - OEIS

A112859

Primes such that the sum of the predecessor and successor primes is divisible by 29.

149, 433, 463, 491, 839, 907, 929, 953, 1217, 1451, 1741, 2789, 2957, 3853, 3917, 4493, 4639, 4957, 5021, 5167, 5227, 5569, 6353, 6673, 6733, 6823, 7219, 7481, 7573, 7649, 7919, 8293, 8443, 8699, 9281, 9421, 9743, 9923, 10151, 10211, 10709, 11161

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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

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 29. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 29.

EXAMPLE

a(1) = 149 because prevprime(149) + nextprime(149) = 139 + 151 = 290 = 29 * 10.

a(2) = 433 because prevprime(433) + nextprime(433) = 431 + 439 = 870 = 29 * 30.

a(3) = 463 because prevprime(463) + nextprime(463) = 461 + 467 = 928 = 29 * 32.

a(4) = 491 because prevprime(491) + nextprime(491) = 487 + 499 = 986 = 29 * 34.

MAPLE

Primes:= select(isprime, [seq(i, i=3..20000, 2)]):

R:= select(t -> Primes[t-1]+Primes[t+1] mod 29 = 0, [$2..nops(Primes)-1]):

Primes[R]; # Robert Israel, May 02 2017

MATHEMATICA

Prime@ Select[Range[2, 1372], Mod[Prime[ # - 1] + Prime[ # + 1], 29] == 0 &] (* Robert G. Wilson v, Jan 05 2006 *)

CROSSREFS