A349304 Terms of sequence A133342 interpreted as numbers written in base 2 and converted here to base 10.

1, 3, 13, 63, 1641, 55979, 1963261, 1051838303, 427823653777, 899765549835411, 962612860717614517, 16451240378526759988983, 275851420933163891499583577, 75079775107059278497058879826395, 1275913767034795679914048924532788093, 1386272923043819758818080175342943182028095

Offset: 0

Author

Bernard Schott, Nov 14 2021

Keywords

• nonn
• base

Comments

a(n) is a Mersenne number (A000225) iff n = 0, 1, 3 (see proof in A133342).

Crossrefs

Cf. A000225, A003590, A007318, A133342.

Programs

Mathematica

a[n_] := FromDigits[Join @@ Table[IntegerDigits[Binomial[n, k], 2], {k, 0, n}], 2]; Array[a, 15, 0] (* Amiram Eldar, Nov 14 2021 *)

PARI

a(n) = fromdigits(concat(vector(n+1, k, binary(binomial(n, k-1)))), 2); \\ Michel Marcus, Nov 14 2021