A381117 Lengths of runs of consecutive primes in A381019.

5, 5, 2, 6, 6, 5, 10, 7, 7, 14, 11, 8, 12, 9, 18, 6, 17, 10, 17, 4, 21, 11, 20, 2, 19, 10, 34, 4, 15, 17, 17, 22, 16, 19, 25, 16, 2, 41, 3, 6, 41, 21, 24, 33, 8, 7, 46, 5, 54, 7, 48, 6, 7, 5, 41, 13, 31, 18, 5, 50, 1, 49, 10, 26, 41, 24, 45, 53, 20, 21, 44, 3

Offset: 1

Author

N. J. A. Sloane, Feb 14 2025

Keywords

• nonn

Comments

For n > 1, a(n) = A381116(n) - A381116(n-1) - 1. (This is a trivial consequence of the definitions.)

Crossrefs

Cf. A381019, A381115, A381116.

Programs

Mathematica

nn = 500; c[_] = False; i = 0; u = v = 2; a[1] = 1;
Monitor[Reap[
  Do[k = u;
    While[Or[c[k],
      ! CoprimeQ[k, Product[a[h], {h, n - Min[k, n - 1], n - 1}] ] ],
    If[k > n - 1, k = v, k++]];
    Set[{a[n], c[k]}, {k, True}];
    If[CompositeQ[k], Sow[i]; i = 0, i++];
    If[k == u, While[c[u], u++]];
If[k == v, While[Or[c[v], CompositeQ[v]], v++]], {n, 2, nn}] ][[-1, 1]], n] (* Michael De Vlieger, Feb 14 2025 *)