S000565


Number of composite numbers between S000564(n) and the next prime number.

1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 9, 9, 9, 9, 11, 9, 9, 11, 9, 11, 13, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 17, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 21, 19, 19, 21, 21, 21, 21, 21, 21, 23, 21, 23

2

S000565

It appears that each positive odd number occurs here about four times.

T. D. Noe, Plot of 499 terms

T. D. Noe, Table of 499 terms

Eric W. Weisstein, MathWorld: Primes Gaps

(Mma) nn = 10000; t = Join[{0}, Table[Total[Transpose[FactorInteger[n]][[2]]], {n, 2, Prime[nn]}]]; t2 = Table[Total[t[[Range[Prime[n] + 1, Prime[n + 1] - 1]]]], {n, nn - 1}]; t3 = Sort[t2]; missing = Complement[Range[t3[[-1]]], t3][[2]]; t4 = Table[Prime[Position[t2, n, 1, 1][[1, 1]]], {n, 2, missing - 1}]; Table[NextPrime[n] - n - 1, {n, t4}]

Cf. S000564.

nonn

T. D. Noe, Apr 06 2015

© Tony D Noe 2014-2015