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 A080377 #13 Feb 09 2025 02:48:29
%S A080377 2,4,6,8,14,10,18,22,34,16,26,32,38,50,62,54,58,46,64,86,82,74,98,106,
%T A080377 94,118,122,128,146,134,142,162,178,158,166,202,194,206,214,218,242,
%U A080377 250,226,254,274,262,256,278,326,302,298,314,382,346,358,338,394,334,386,362,398,446,454,486
%N A080377 Prime gaps where A080374 increases.
%C A080377 a(n+1) is the smallest prime gap (A001223) that has a prime factor not present in previous gaps or was present but at a lower power.
%F A080377 a(n) = prime(1+A080376(n)) - prime(A080376(n)).
%e A080377 18 is the 7th term: in the first 6 terms, {2, 4, 6, 8, 14, 10}, 3 does not occur with power 2 unlike in 18 = 2 * 3^2.
%e A080377 22 is the 8th term: in the first 7 terms 11 is not a prime factor unlike 22.
%e A080377 Several even numbers do not arise in this sequence, e.g., 12, 20, 36, 48, etc..
%t A080377 s=1; Do[s1=s; s=LCM[s, d=Prime[n+1]-Prime[n]]; If[Greater[s, s1], Print[d]], {n, 1, 10000000}]
%Y A080377 Cf. A001223, A080374, A080375, A080376.
%K A080377 nonn
%O A080377 1,1
%A A080377 _Labos Elemer_, Feb 27 2003
%E A080377 More terms from _Amiram Eldar_, Feb 09 2025