A390233 Numbers k such that A178854(k) = A178854(k+1).

1, 5, 8, 13, 17, 19, 20, 22, 24, 25, 26, 31, 33, 40, 41, 42, 43, 47, 50, 54, 55, 58, 63, 66, 69, 71, 75, 78, 79, 80, 81, 83, 84, 86, 87, 92, 94, 96, 99, 100, 103, 105, 108, 109, 110, 111, 113, 115, 116, 119, 120, 123, 124

Offset

1,2

Comments

Numbers k such that Catalan(2^k-1) mod 2^k = Catalan(2^(k+1)-1) mod 2^(k+1).

Links

Table of n, a(n) for n=1..53.

Mathematica

okQ[k_]:=Mod[CatalanNumber[2^k-1], 2^k]==Mod[CatalanNumber[2^(k+1)-1], 2^(k+1)]; Select[Range[25], okQ] (* James C. McMahon, Jan 21 2026 *)

Crossrefs

Cf. A000108, A038003, A178854.

Sequence in context: A314424 A314425 A058240 * A097268 A226696 A391423

Adjacent sequences: A390230 A390231 A390232 * A390234 A390235 A390236

Keyword

nonn,hard,more

Author

Chai Wah Wu, Jan 20 2026

Extensions

a(15)-a(35) from Chai Wah Wu, Apr 25 2026

a(36)-a(53) from Chai Wah Wu, May 07 2026

Status

approved