A368404 -id:A368404 - cp's OEIS frontend

A368402 Numbers k such that k and k+1 are both in A268375.

1, 2, 3, 4, 7, 8, 11, 12, 16, 17, 18, 19, 27, 28, 31, 43, 44, 47, 48, 49, 52, 63, 67, 75, 79, 80, 97, 98, 112, 116, 124, 127, 147, 148, 162, 163, 171, 172, 175, 191, 192, 207, 211, 241, 242, 243, 244, 256, 268, 271, 283, 288, 292, 316, 324, 331, 332, 337, 367

Offset: 1

Amiram Eldar, Dec 23 2023

Analogous to A342028, as A268375 is analogous to A130091.

The Mersenne primes (A000668) are terms.

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

Subsequence of A130091, A268375 and A342028.

Subsequences: A000668, A368403, A368404.

f[e_] := Position[Reverse[IntegerDigits[e, 2]], 1] // Flatten; q[n_] := q[n] = UnsameQ @@ Flatten[f /@ FactorInteger[n][[;; , 2]]]; Select[Range[100], q[#] && q[#+1] &]

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(is1 = 0, is2); for(k = 1, kmax, is2 = isA268375(k); if(is1 && is2, print1(k-1, ", ")); is1 = is2);}

A368403 Starts of runs of 3 consecutive integers in A268375.

Original entry on oeis.org

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++); }

cp's OEIS Frontend

A368402 Numbers k such that k and k+1 are both in A268375.

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