A381117 - OEIS

%I #10 Feb 14 2025 10:19:53

%S 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,

%T 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,

%U 5,41,13,31,18,5,50,1,49,10,26,41,24,45,53,20,21,44,3

%N Lengths of runs of consecutive primes in A381019.

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

%t nn = 500; c[_] = False; i = 0; u = v = 2; a[1] = 1;

%t Monitor[Reap[

%t   Do[k = u;

%t     While[Or[c[k],

%t       ! CoprimeQ[k, Product[a[h], {h, n - Min[k, n - 1], n - 1}] ] ],

%t     If[k > n - 1, k = v, k++]];

%t     Set[{a[n], c[k]}, {k, True}];

%t     If[CompositeQ[k], Sow[i]; i = 0, i++];

%t     If[k == u, While[c[u], u++]];

%t If[k == v, While[Or[c[v], CompositeQ[v]], v++]], {n, 2, nn}] ][[-1, 1]], n] (* _Michael De Vlieger_, Feb 14 2025 *)

%Y Cf. A381019, A381115, A381116.

%K nonn,new

%O 1,1

%A _N. J. A. Sloane_, Feb 14 2025