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

Author

Amiram Eldar, Dec 23 2023

Keywords

• nonn
• base

Comments

Analogous to A342028, as A268375 is analogous to A130091.

The Mersenne primes (A000668) are terms.

Links

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

Crossrefs

Subsequence of A130091, A268375 and A342028.

Subsequences: A000668, A368403, A368404.

Programs

Mathematica

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] &]

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