A368404 Starts of runs of 4 consecutive integers in A268375.

1, 2, 16, 17, 47, 241, 242, 1249, 4049, 120049, 3693761, 14268481, 22997761, 28140001, 35296801, 83747681, 91801249, 256692481, 971435041, 1261928321, 1429948241, 1691176481, 1697230321, 2168901521, 3018800401, 4199128081, 5795553121, 7626372001, 7940268161, 11438281249

Offset: 1

Author

Amiram Eldar, Dec 23 2023

Keywords

• nonn
• base

Comments

Analogous to A342030, as A268375 is analogous to A130091.

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?

Crossrefs

Subsequence of A130091, A268375, A342030, A368402 and A368403.

Programs

Mathematica

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]

PARI

isA268375(n) = {my(e = factor(n)[,2], b = 0); for(i=1, #e, b = bitor(b, e[i])); n == 1 || b == vecsum(e);}
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++);}