A006695 a(2n)=2*a(2n-2)^2-1, a(2n+1)=2*a(2n)-1, a(0)=2. (Formerly M0838)

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

Offset

0,1

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A192611 A254461 A048463 * A128157 A259488 A372229

Adjacent sequences: A006692 A006693 A006694 * A006696 A006697 A006698

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved