A368402 -id:A368402 - cp's OEIS frontend

A368403 Starts of runs of 3 consecutive integers in A268375.

1, 2, 3, 7, 11, 16, 17, 18, 27, 43, 47, 48, 79, 97, 147, 162, 171, 191, 241, 242, 243, 331, 367, 387, 431, 507, 547, 603, 907, 1051, 1249, 1250, 1619, 1871, 2267, 2347, 2523, 2799, 3411, 3643, 3987, 4049, 4050, 4111, 4175, 4203, 4491, 4923, 5119, 5391, 5407, 6091

Offset: 1

Amiram Eldar, Dec 23 2023

Analogous to A342029, as A268375 is analogous to A130091.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Subsequence of A130091, A268375, A342029 and A368402.

A368404 is a subsequence.

f[e_] := Position[Reverse[IntegerDigits[e, 2]], 1] // Flatten; q[n_] := UnsameQ @@ Flatten[f /@ FactorInteger[n][[;; , 2]]]; q[0] = False; seq[kmax_] := Module[{m = 3, 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[6000]

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(tri = vector(3, i, isA268375(i)), k = 4); while(k < kmax, if(vecsum(tri) == 3, print1(k-3, ", ")); tri = concat(vecextract(tri, "^1"), isA268375(k)); k++); }

A368404 Starts of runs of 4 consecutive integers in A268375.

Original entry on oeis.org

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

Amiram Eldar, Dec 23 2023

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?

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

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]

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++);}

cp's OEIS Frontend

A368403 Starts of runs of 3 consecutive integers in A268375.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI