login
Starts of run of 3 consecutive integers that are all terms of A360902.
3

%I #9 Feb 26 2023 03:26:50

%S 7939375,12799375,20410623,30466287,56661199,83365119,105146991,

%T 197479375,235838223,259360623,293380623,555499375,657880623,

%U 691579375,871374591,871720623,953280495,975079375,996393391,1032100623,1047979375,1096579375,1348000623,1355419375

%N Starts of run of 3 consecutive integers that are all terms of A360902.

%H Amiram Eldar, <a href="/A360905/b360905.txt">Table of n, a(n) for n = 1..300</a>

%e 7939375 is a term since A034444(7939375) = A005361(7939375) = 4, A034444(7939376) = A005361(7939376) = 4, and A034444(7939377) = A005361(7939377) = 4.

%t q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Times @@ e == 2^Length[e]]; q[1] = True; seq[kmax_] := Module[{tri = q /@ Range[3], s = {}, k = 4}, While[k < kmax, If[And @@ tri, AppendTo[s, k - 3]]; tri = Join[Rest[tri], {q[k]}]; k++]; s]; seq[10^7]

%o (PARI) is(k) = {my(e = factor(k)[,2]); prod(i = 1, #e, e[i]) == 2^#e; }

%o lista(kmax) = {my(tri = vector(3, i, is(i)), k = 4); while(k < kmax, if(vecsum(tri) == 3, print1(k-3, ", ")); tri = concat(vecextract(tri, "^1"), is(k)); k++); }

%Y Subsequence of A360902 and A360903.

%Y Cf. A005361, A034444.

%K nonn

%O 1,1

%A _Amiram Eldar_, Feb 25 2023