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 A098968 #12 May 25 2025 11:54:44
%S A098968 0,1,2,4,8,10,12,16,22,26,38,40,42,46,48,54,56,70,74,78,80,98,112,114,
%T A098968 124,136,138,158,188,198,232,234,244,246,268,304,326,328,334,338,370
%N A098968 Record values for size of sea of composite numbers surrounding primes.
%C A098968 For a prime p let s(p) (essentially A046930) denote the number of composite numbers less than p and greater than max{1, previous prime} or greater than p and less than the next prime. Sequence gives record values of s(p).
%t A098968 a = {1, 2}; b = {0, 1}; d = 1; p = 2; q = 3; Do[ r = Prime[n]; c = r - p - 2; If[c > d, Print[{n + 1, c}]; d = c; AppendTo[a, n - 1]; AppendTo[b, c]]; p = q; q = r, {n, 3, 10^9}]; b (* _Robert G. Wilson v_, Oct 27 2004 *)
%t A098968 Join[{0},DeleteDuplicates[Total/@Partition[Differences[Prime[Range[5*10^6]]]-1,2,1],GreaterEqual]] (* The program generates the first 34 terms of the sequence. *) (* _Harvey P. Dale_, May 25 2025 *)
%Y A098968 Records in A046930 (if initial term is 0 not 1). Cf. A098969, A046931.
%K A098968 nonn
%O A098968 0,3
%A A098968 _N. J. A. Sloane_, Oct 24 2004
%E A098968 More terms from _Robert G. Wilson v_ and _Olaf Voß_, Oct 27 2004