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A006695 a(2n)=2*a(2n-2)^2-1, a(2n+1)=2a(2n)-1, a(0)=2.
(Formerly M0838)
2
2, 3, 7, 13, 97, 193, 18817, 37633, 708158977, 1416317953, 1002978273411373057, 2005956546822746113, 2011930833870518011412817828051050497, 4023861667741036022825635656102100993 (list; graph; refs; listen; history; text; internal format)
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

S. Kalpazidou et al., Luroth [ Lueroth ]-type alternating series representations for real numbers, Acta Arithmetica, 55 (1990), 311-322.

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., L├╝roth-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

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

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

Cf. A001685, A002715, A003686, A064526.

Sequence in context: A192611 A254461 A048463 * A128157 A259488 A073827

Adjacent sequences:  A006692 A006693 A006694 * A006696 A006697 A006698

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 22 18:31 EDT 2019. Contains 328319 sequences. (Running on oeis4.)