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

1,1

Comments

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

Links

Table of n, a(n) for n=1..72.

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 *)

Crossrefs

Cf. A381019, A381115, A381116.

Sequence in context: A132376 A273007 A316168 * A019602 A153839 A378204

Adjacent sequences: A381113 A381115 A381116 * A381118 A381119 A381120

Keyword

nonn,new

Author

N. J. A. Sloane, Feb 14 2025

Status

approved