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 A107926 #114 Feb 16 2025 08:32:57
%S A107926 4,8,18,16,54,48,50,108,102,44,234,444,98,228,174,92,414,432,242,516,
%T A107926 582,256,1182,672,406,612,846,272,1038,984,442,1776,1902,292,1074,636,
%U A107926 1054,3312,1122,476,1398,1464,530,1728,2730,572,2706,3348,682,2844,3342
%N A107926 The least number k such that there are primes p and q with p - q = 2*n, p + q = k, and p the least such prime >= k/2.
%C A107926 From the Goldbach conjecture.
%C A107926 A107926 = 2*A103147 by definition.
%C A107926 a(3n)> a(3n-2), a(3n-1), a(3n+1) & a(3n+2) for all n > 0 except for n = 1, 2, 12, 19, 20 or 41.
%C A107926 Of those values found so far a(3n+2) > a(3n+1) by ~8%. - _Robert G. Wilson v_, Nov 03 2013
%C A107926 Except for 1, all indices, i, not congruent to 0 (mod 3), a(i) is congruent to 0 (mod 6) and for all indices, i, congruent to 0 (mod 3), a(i) is not congruent to 0 (mod 6). Of those not congruent to 0 (mod 6), those congruent to 2 outnumber those congruent to 4, about 8 to 7. _Robert G. Wilson v_, Nov 03 2013
%H A107926 Robert G. Wilson v, <a href="/A107926/b107926.txt">Table of n, a(n) for n = 0..2560</a> (first 501 terms from T. D. Noe)
%H A107926 Mark Herkommer, <a href="http://www.petrospec-technologies.com/Herkommer/goldbach.htm">Goldbach Conjecture Research</a>.
%H A107926 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/goldbach.html">Goldbach conjecture verification</a>.
%H A107926 The Prime Glossary, <a href="https://t5k.org/glossary/xpage/goldbachconjecture.html">Goldbach's conjecture</a>
%H A107926 +Plus Magazine ... living mathematics, <a href="http://plus.maths.org/content/mathematical-mysteries-goldbach-conjecture">Mathematical mysteries: the Goldbach conjecture</a>
%H A107926 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachConjecture.html">Goldbach Conjecture</a>
%H A107926 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach's_conjecture">Goldbach conjecture</a>
%e A107926 a(0) = 4 because 4=2+2 and 2-2=0.
%e A107926 a(1) = 8 because 8 is the least number with 8=p+q and p-q=2 for primes p and q.
%e A107926 a(2) = 18 because 18=7+11 and the primes 7 and 11 have difference 4.
%t A107926 f[n_] := For[p = n/2, True, p--, If[PrimeQ[p] && PrimeQ[n - p], Return[n/2 - p]]]; nn=101; t=Table[0,{nn}]; cnt=0; n=1; While[cnt<nn, n++; d=f[2n]; If[d+1<=nn && t[[d+1]]==0, t[[d+1]]=n; cnt++]]; 2t
%Y A107926 Cf. A066285, A103147, records in A065978 and A066286.
%K A107926 nonn
%O A107926 0,1
%A A107926 Gilmar J. Rodriguez (Gilmar.Rodriguez(AT)nwfwmd.state.fl.us) and _Robert G. Wilson v_, Jun 16 2005