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A112859 Primes such that the sum of the predecessor and successor primes is divisible by 29. 20
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 (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

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

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

Sequence in context: A142359 A185692 A216312 * A141980 A023290 A142629

Adjacent sequences:  A112856 A112857 A112858 * A112860 A112861 A112862

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 25 11:48 EDT 2017. Contains 288709 sequences.