A105850 a(n+1) = a(n)^2 - 2^(2^n+1) with a(1) = 8.

8, 56, 3104, 9634304, 92819813433344, 8615517765800787268541087744, 74227146372828989101844394431169040459931374583287906304

Offset

1,1

Comments

Lehmer used this sequence in his proof of the Lucas-Lehmer test.

Links

Table of n, a(n) for n=1..7.

D. H. Lehmer, On Lucas's Test for the Primality of Mersenne's Numbers, J. London Math. Soc., 10 (1935) 162-165.

Formula

a(n) = 2^(2^(n-1))*A003010(n).

Mathematica

nxt[{n_, a_}]:={n+1, a^2-2^(2^n+1)}; Transpose[NestList[nxt, {1, 8}, 7]][[2]] (* Harvey P. Dale, Jul 24 2013 *)

Crossrefs

Cf. A003010.

Sequence in context: A133671 A326239 A154411 * A009089 A296466 A202863

Adjacent sequences: A105847 A105848 A105849 * A105851 A105852 A105853

Keyword

nonn

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Apr 22 2005

Status

approved