A006695 a(2n)=2*a(2n-2)^2-1, a(2n+1)=2*a(2n)-1, a(0)=2.

2, 3, 7, 13, 97, 193, 18817, 37633, 708158977, 1416317953, 1002978273411373057, 2005956546822746113, 2011930833870518011412817828051050497, 4023861667741036022825635656102100993

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

An infinite coprime sequence defined by recursion.

Every term is relatively prime to all others. - Michael Somos, Feb 01 2004

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n=0..19
• S. Kalpazidou et al., Lüroth-type alternating series representations for real numbers, Acta Arithmetica, 55 (1990), 311-322.
• Jeffrey Shallit, Rational numbers with non-terminating, non-periodic modified Engel-type expansions, Fib. Quart., 31 (1993), 37-40.
• Index entries for sequences related to Engel expansions

Crossrefs

Cf. A001075, A001685, A002715, A003686, A064526.

Programs

Mathematica

nxt[{n_,a_,b_}]:=If[OddQ[n],{n+1,b,2a^2-1},{n+1,b,2b-1}]; Transpose[ NestList[ nxt,{1,2,3},15]][[2]] (* Harvey P. Dale, Jun 22 2015 *)

PARI

a(n)=if(n<1,2*(n==0),if(n%2,2*a(n-1)-1,2*a(n-2)^2-1))

Formula

a(2n) = A001075(2^n).