A124589 - OEIS

%I #17 Mar 13 2020 16:46:17

%S 2,3,5,7,11,13,17,19,29,37,41,43,59,67,71,79,97,101,103,107,109,127,

%T 137,149,163,179,191,193,197,223,227,229,239,269,277,281,307,311,313,

%U 347,349,379,397,419,431,439,457,461,463,487,499,521,569,599,613,617,641,643,659

%N Primes p such that q-p <= 4, where q is the next prime after p.

%C Union of A124588 and A029710; complement of A124582. - _Reinhard Zumkeller_, Dec 23 2006

%H R. Zumkeller, <a href="/A124589/b124589.txt">Table of n, a(n) for n = 1..1000</a>

%H K. Soundararajan, <a href="https://doi.org/10.1090/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.

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>

%F a(n) >> n log^2 n. Infinite under standard conjectures. - _Charles R Greathouse IV_, Jun 01 2016

%t Transpose[Select[Partition[Prime[Range[200]],2,1],Last[#]-First[#]<5&]][[1]] (* _Harvey P. Dale_, Apr 22 2013 *)

%o (PARI) is(n)=isprime(n) && (isprime(n+2) || isprime(n+4) || n==2) \\ _Charles R Greathouse IV_, Jun 01 2016

%Y CF. A029710, A124582, A124588.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 19 2006