A085613 a(n) = 2^(n-1) + (2 + (-1)^n)^((n-2)/2).

2, 3, 5, 11, 17, 41, 65, 155, 257, 593, 1025, 2291, 4097, 8921, 16385, 34955, 65537, 137633, 262145, 543971, 1048577, 2156201, 4194305, 8565755, 16777217, 34085873, 67108865, 135812051, 268435457, 541653881, 1073741825, 2161832555, 4294967297, 8632981313

Offset: 1

Author

Ben de la Rosa & Johan Meyer (MeyerJH.sci(AT)mail.uovs.ac.za), Jul 09 2003

Keywords

• nonn
• easy

Comments

Extends Euler's 6-term sequence.

In Euler's 6-term sequence we have noticed that e(1) = 2 = 2^0 + 1; e(2) = 3 = 2^1 + 3^0; e(3) = 5 = 2^2 + 1; e(4) = 11 = 2^3 + 3^1; e(5) = 17 = 2^4 + 1; e(6) = 41 = 2^5 + 3^2, which of course immediately leads to our formula above. Note: For m>0, we take m^(1/2) to be the unique positive square root of m.

a(2^n + 1), n=0,1,2,... are the Fermat numbers.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,4,-8,-3,6).

Crossrefs

Cf. A082605.

Programs

PARI

a(n) = 2^(n-1) + (2 + (-1)^n)^((n-2)/2) \\ Charles R Greathouse IV, Jan 29 2013

Extensions

More terms from Neven Juric, Apr 10 2008