This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A124589 #17 Mar 13 2020 16:46:17 %S A124589 2,3,5,7,11,13,17,19,29,37,41,43,59,67,71,79,97,101,103,107,109,127, %T A124589 137,149,163,179,191,193,197,223,227,229,239,269,277,281,307,311,313, %U A124589 347,349,379,397,419,431,439,457,461,463,487,499,521,569,599,613,617,641,643,659 %N A124589 Primes p such that q-p <= 4, where q is the next prime after p. %C A124589 Union of A124588 and A029710; complement of A124582. - _Reinhard Zumkeller_, Dec 23 2006 %H A124589 R. Zumkeller, <a href="/A124589/b124589.txt">Table of n, a(n) for n = 1..1000</a> %H A124589 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 A124589 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a> %F A124589 a(n) >> n log^2 n. Infinite under standard conjectures. - _Charles R Greathouse IV_, Jun 01 2016 %t A124589 Transpose[Select[Partition[Prime[Range[200]],2,1],Last[#]-First[#]<5&]][[1]] (* _Harvey P. Dale_, Apr 22 2013 *) %o A124589 (PARI) is(n)=isprime(n) && (isprime(n+2) || isprime(n+4) || n==2) \\ _Charles R Greathouse IV_, Jun 01 2016 %Y A124589 CF. A029710, A124582, A124588. %K A124589 nonn %O A124589 1,1 %A A124589 _N. J. A. Sloane_, Dec 19 2006