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

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

Offset: 1

Author

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

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A003010.

Programs

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 *)

Formula

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