A207976 a(1) = 2; for n>1, a(n) = largest integer such that the sequence b(n) = a(n)^(1/n) is decreasing.

2, 3, 5, 8, 13, 21, 34, 56, 92, 152, 251, 414, 684, 1130, 1867, 3084, 5095, 8418, 13908, 22979, 37966, 62727, 103638, 171232, 282911, 467429, 772292, 1275990, 2108206, 3483204, 5754993, 9508472, 15710018

Offset

1,1

Comments

(n -> oo) lim (log a(n+1)/log a(n))^n = e. - Thomas Ordowski, Oct 06 2014

Links

Table of n, a(n) for n=1..33.

Formula

a(1) = 2, a(2) = 3; a(n+1) = floor( a(n)^(1+1/n) ) for n > 1.

a(n) = 1 + floor(q^n), where q = lim a(n+1)/a(n) = 1.652213...

a(2) = 3; a(n) = floor( exp( (n/(n-1)) * log a(n-1) ) ) for n > 2.

Maple

A207976 := proc(n)
    if n = 1 then
        2;
    elif n = 2 then
        3;
    else
        floor( exp(n/(n-1)*log(procname(n-1))) );
    end if;
end proc: # R. J. Mathar, Mar 22 2012

Prog

(PARI) {a(n) = if( n<3, max(1, n+1), floor( exp( log(a(n-1)) * n/(n-1) )))}; /* Michael Somos, Oct 06 2014 */

Crossrefs

Sequence in context: A042581 A349843 A302019 * A093332 A254786 A050762

Adjacent sequences: A207973 A207974 A207975 * A207977 A207978 A207979

Keyword

nonn

Author

Thomas Ordowski, Feb 20 2012

Status

approved