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A124596 Primes p such that q-p = 30, where q is the next prime after p. 9
4297, 4831, 5351, 5749, 6491, 6917, 7253, 7759, 7963, 8389, 8893, 13063, 13187, 13933, 13967, 14251, 14983, 16381, 16573, 17627, 18553, 18869, 20563, 21283, 21347, 21617, 23633, 23689, 24251, 25189, 26053, 26597, 27299, 27367, 27551, 28319, 28979, 29537 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These are the primes p = prime(k) where A001223(k) = 30. - N. J. A. Sloane, Dec 25 2019

Primes p such that r-q=q-p=30, where p, q, r are three successive primes, are A052195 = (69593, 110651, 134609, 228647, 237791, 250889, 303157, 24907,...). Primes p such that s-r=r-q=q-p=30, where p, q, r, s are four successive primes, are A052243 = (642427, 1058861, 3431903, 4176587, 4560121, 4721047, 5072269, 5145403, ...). - Zak Seidov, Dec 20 2006, edited by M. F. Hasler, Apr 04 2013

LINKS

Remi Eismann, Table of n, a(n) for n = 1..10000

K. Soundararajan, Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc., 44 (2007), 1-18. DOI: 10.1090/S0273-0979-06-01142-6

K. Soundararajan, Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim, arXiv:math/0605696 [math.NT], 2006.

Index entries for primes, gaps between

MATHEMATICA

max = 30000;

Reap[For[p = 2; q = 3, p < max, p = q, q = NextPrime[p]; If[q - p == 30, Sow[p]]]][[2, 1]] (* Jean-Fran├žois Alcover, Sep 02 2018 *)

Select[Partition[Prime[Range[5000]], 2, 1], #[[2]]-#[[1]]==30&][[All, 1]] (* Harvey P. Dale, Dec 25 2019 *)

CROSSREFS

Cf. A001223, A052195, A052243.

See also A052187 and references therein.

Sequence in context: A204400 A271104 A234164 * A224522 A210263 A165067

Adjacent sequences:  A124593 A124594 A124595 * A124597 A124598 A124599

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 19 2006

STATUS

approved

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Last modified November 30 05:31 EST 2020. Contains 338781 sequences. (Running on oeis4.)