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

0,3

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).

Links

Table of n, a(n) for n=0..40.

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 *)

Crossrefs

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

Sequence in context: A166245 A276623 A121519 * A032368 A134533 A089953

Adjacent sequences: A098965 A098966 A098967 * A098969 A098970 A098971

Keyword

nonn

Author

N. J. A. Sloane, Oct 24 2004

Extensions

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

Status

approved