A397165 - OEIS

%I #10 Jun 17 2026 15:46:48

%S 33,120,171,201,203,210,213,230,238,264,286,288,294,322,354,373,395,

%T 479,486,506,542,553,563,583,609,628,646,659,688,700,719,724,730,744,

%U 749,770,814,862,883,963,975,1009,1020,1056,1103,1115,1119,1182,1247,1260,1273,1324,1358

%N Apply PrimePi to A397164.

%C These are the indices of the primes in A280864 that begin a block of length 4 that both begins and ends with a prime.

%H Michael De Vlieger, <a href="/A397165/b397165.txt">Table of n, a(n) for n = 1..2856</a>

%t Block[{c, j, k, m, q, r, s, t, w, nn, rad},

%t   nn = 24000; c[_] := False; q = 0; r = s = 1; t = {};

%t   rad[n_] := rad[n] = Times @@ FactorInteger[n][[All, 1]];

%t   Monitor[Reap[Do[w = GCD[r, s]; m = r/w; k = m;

%t     While[Or[c[k], ! CoprimeQ[w, k]], k += m];

%t       c[k] = True; s = r; r = rad[k];

%t     If[CoprimeQ[s, r],

%t       If[Length[t] == 4,

%t         If[AllTrue[{First[t], Last[t]}, PrimeQ], Sow[PrimePi@ First[t] ] ] ];

%t       q++; t = {k}, AppendTo[t, k] ], {i, nn}] ][[-1, 1]], i] ] (* _Michael De Vlieger_, Jun 17 2026 *)

%Y Cf. A000720, A280774, A280864, A283832, A396300, A396301, A397102, A397164.

%K nonn,new

%O 1,1

%A _N. J. A. Sloane_, Jun 17 2026