A098968 Record values for size of sea of composite numbers surrounding primes.

0, 1, 2, 4, 8, 10, 12, 16, 22, 26, 38, 40, 42, 46, 48, 54, 56, 70, 74, 78, 80, 98, 112, 114, 124, 136, 138, 158, 188, 198, 232, 234, 244, 246, 268, 304, 326, 328, 334, 338, 370

Offset: 0

Author

N. J. A. Sloane, Oct 24 2004

Keywords

• nonn

Comments

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).

Crossrefs

Records in A046930 (if initial term is 0 not 1). Cf. A098969, A046931.

Programs

Mathematica

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 *)
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 *)

Extensions

More terms from Robert G. Wilson v and Olaf Voß, Oct 27 2004