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A064183 Define a pair of sequences by p(0)=0, q(0)=p(1)=q(1)=1, q(n+1)=p(n)*q(n-1), p(n+1)=q(n+1)+q(n) for n>0; sequence give q(n); A064526 gives p(n). 3
1, 1, 1, 2, 3, 10, 39, 490, 20631, 10349290, 213941840151, 2214253254659846890, 473721461633379426414550183191, 1048939288228833100615882755549676600679754298090 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..13.

M. Somos and R. Haas, A linked pair of sequences implies the primes are infinite, Amer. Math. Monthly, 110 (No. 6, 2003), 539-540.

FORMULA

a(n) = (a(n-1)+a(n-2))*a(n-2).

lim n->infinity a(n)/a(n-1)^Phi = 1 - Gerald McGarvey, Aug 29 2004

a(n) ~ c^(phi^n), where c = 1.23642417842410860616065684299168229758826316461949675490684055924721259... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, May 21 2015

MATHEMATICA

Flatten[{1, RecurrenceTable[{a[n]==(a[n-1]+a[n-2])*a[n-2], a[1]==1, a[2]==1}, a, {n, 1, 10}]}] (* Vaclav Kotesovec, May 21 2015 *)

PROG

(PARI) {a(n) = local(v); if( n<3, n>=0, v = [1, 1]; for( k=3, n, v = [v[2], v[1] * (v[1] + v[2])]); v[2])}

(PARI) {a(n) = if( n<3, n>=0, (a(n-1) + a(n-2)) * a(n-2))}

CROSSREFS

Cf. A064526, A236394.

Sequence in context: A164933 A003048 A008980 * A050381 A129716 A032293

Adjacent sequences:  A064180 A064181 A064182 * A064184 A064185 A064186

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Sep 20 2001

STATUS

approved

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Last modified November 14 03:52 EST 2018. Contains 317159 sequences. (Running on oeis4.)