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%I #5 Dec 24 2023 02:42:45
%S 1,2,16,17,47,241,242,1249,4049,120049,3693761,14268481,22997761,
%T 28140001,35296801,83747681,91801249,256692481,971435041,1261928321,
%U 1429948241,1691176481,1697230321,2168901521,3018800401,4199128081,5795553121,7626372001,7940268161,11438281249
%N Starts of runs of 4 consecutive integers in A268375.
%C Analogous to A342030, as A268375 is analogous to A130091.
%C 1, 16 and 241 are the only starts of runs of 5 consecutive integers in A268375 below 10^10. Are there any other such runs?
%t f[e_] := Position[Reverse[IntegerDigits[e, 2]], 1] // Flatten; q[n_] := UnsameQ @@ Flatten[f /@ FactorInteger[n][[;; , 2]]]; q[0] = False; seq[kmax_] := Module[{m = 4, s = {}, v}, v = q /@ Range[0, m - 1]; Do[v = Join[Rest[v], {q[k]}]; If[And @@ v, AppendTo[s, k - m + 1]], {k, m, kmax}]; s]; seq[5000]
%o (PARI) isA268375(n) = {my(e = factor(n)[,2], b = 0); for(i=1, #e, b = bitor(b, e[i])); n == 1 || b == vecsum(e);}
%o lista(kmax) = {my(quad = vector(4, i, isA268375(i)), k = 5); while(k < kmax, if(vecsum(quad) == 4, print1(k-4, ", ")); quad = concat(vecextract(quad, "^1"), isA268375(k)); k++);}
%Y Subsequence of A130091, A268375, A342030, A368402 and A368403.
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Dec 23 2023
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