cp's OEIS Frontend

A124596 Primes p such that q-p = 30, where q is the next prime after p.

%I A124596 #31 Dec 25 2019 13:50:04
%S A124596 4297,4831,5351,5749,6491,6917,7253,7759,7963,8389,8893,13063,13187,
%T A124596 13933,13967,14251,14983,16381,16573,17627,18553,18869,20563,21283,
%U A124596 21347,21617,23633,23689,24251,25189,26053,26597,27299,27367,27551,28319,28979,29537
%N A124596 Primes p such that q-p = 30, where q is the next prime after p.
%C A124596 These are the primes p = prime(k) where A001223(k) = 30. - _N. J. A. Sloane_, Dec 25 2019
%C A124596 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
%H A124596 Remi Eismann, <a href="/A124596/b124596.txt">Table of n, a(n) for n = 1..10000</a>
%H A124596 K. Soundararajan, <a href="http://www.ams.org/journals/bull/2007-44-01/S0273-0979-06-01142-6/">Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim</a>, Bull. Amer. Math. Soc., 44 (2007), 1-18. DOI: 10.1090/S0273-0979-06-01142-6
%H A124596 K. Soundararajan, <a href="http://arxiv.org/abs/math/0605696">Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim</a>, arXiv:math/0605696 [math.NT], 2006.
%H A124596 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%t A124596 max = 30000;
%t A124596 Reap[For[p = 2; q = 3, p < max, p = q, q = NextPrime[p]; If[q - p == 30, Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Sep 02 2018 *)
%t A124596 Select[Partition[Prime[Range[5000]],2,1],#[[2]]-#[[1]]==30&][[All,1]] (* _Harvey P. Dale_, Dec 25 2019 *)
%Y A124596 Cf. A001223, A052195, A052243.
%Y A124596 See also A052187 and references therein.
%K A124596 nonn
%O A124596 1,1
%A A124596 _N. J. A. Sloane_, Dec 19 2006