A126884 a(n) = (2^0)*(2^1)*(2^2)*(2^3)...(2^n)+1 = 2^T_n+1 (cf. A000217).

2, 3, 9, 65, 1025, 32769, 2097153, 268435457, 68719476737, 35184372088833, 36028797018963969, 73786976294838206465, 302231454903657293676545, 2475880078570760549798248449, 40564819207303340847894502572033, 1329227995784915872903807060280344577, 87112285931760246646623899502532662132737

Offset: 0

Author

Marco Matosic, Dec 29 2006

Keywords

• nonn
• easy

Comments

For n>1 every odd/even pair share at least one factor.

Crossrefs

Cf. A000217, A006125.

Programs

Maple

a:= n-> 2^(n*(n+1)/2)+1:
seq(a(n), n=0..16);  # Alois P. Heinz, Jun 20 2020

Mathematica

Table[Times@@(2^Range[0,n])+1,{n,0,20}] (* Harvey P. Dale, Aug 10 2021 *)

PARI

a(n) = prod(k=0, n, 2^k) + 1  \\ Michel Marcus, Jul 16 2013

Formula

a(n) = 2^A000217(n)+1. - Michel Marcus, Jul 16 2013

a(n) = A006125(n+1)+1. - Alois P. Heinz, Jun 20 2020

Extensions

a(11) corrected and a(14-16) from Georg Fischer, Jun 20 2020