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

1,2

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?

Links

Table of n, a(n) for n=1..30.

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]

Prog

(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++); }

Crossrefs

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

Sequence in context: A032935 A004831 A342030 * A217307 A282408 A282838

Adjacent sequences: A368401 A368402 A368403 * A368405 A368406 A368407

Keyword

nonn,base

Author

Amiram Eldar, Dec 23 2023

Status

approved