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 A074259 #25 Dec 23 2024 14:53:42
%S A074259 1,2,6,12,6,12,12,30,6,24,18,42,6,12,42,6,12,30,12,66,60,12,12,48,18,
%T A074259 84,48,12,6,24,36,24,18,48,102,42,60,6,12,18,54,120,6,60,120,30,12,30,
%U A074259 18,12,48
%N A074259 Gaps between primes p such that 2p+1 is also prime, i.e., Sophie-Germain primes A005384.
%C A074259 The first two consecutive identical gaps are 12, 12 between A005384(6..8) = (29, 41, 53).
%C A074259 The first three, four and five identical gaps in a row are equal to 30, 150 and 420, respectively, and occur after A005384(85) = 3299, A005384(29952) = 4866623, and A005384(32361449747) = 22081407211439. These were found by N. Fernandez and G. Resta, see link to discussion on the SeqFan mailing list. - _M. F. Hasler_, Sep 18 2016
%H A074259 M. F. Hasler, <a href="/A074259/b074259.txt">Table of n, a(n) for n = 1..7745</a>
%H A074259 Giovanni Resta, in reply to Harvey P. Dale and others, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2016-September/016776.html">Re: Consecutive Sophie Germain primes with the same gap</a>, SeqFan mailing list, Sep. 2016. (Click "Previous message" to see <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2016-September/016771.html">Neil Fernandez' earlier results</a>.)
%t A074259 Select[Prime[Range[500]],PrimeQ[2#+1]&]//Differences (* _Harvey P. Dale_, Jul 15 2019 *)
%o A074259 (PARI) c=0; forprime(p=1+L=2,10^6,if(isprime(2*p+1),write("primegap.txt",c++," "p-L); L=p)) \\ Edited by _M. F. Hasler_, Sep 16 2016
%Y A074259 First differences of A005384.
%K A074259 nonn
%O A074259 1,2
%A A074259 _Jon Perry_, Sep 20 2002
%E A074259 Edited (name, offset, more terms) by _M. F. Hasler_, Sep 16 2016