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A073414 Numerator of the n-th convergent to Sum_{k>=0} 1/2^(2^k). 3
0, 1, 4, 9, 40, 169, 1054, 4385, 9824, 43681, 271910, 587501, 2621914, 16318985, 67897854, 287910401, 643718656, 2862785025, 17820428806, 38503642637, 171834999354, 725843640053, 4526896839672, 18833430998741, 42193758837154 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Robert Israel, Table of n, a(n) for n = 1..1650

FORMULA

a(n) = a(n-1) A007400(n-1) + a(n-2). - Robert Israel, Jun 14 2016

MAPLE

a007400:= proc(n) option remember; local n8, n16;

    n8:= n mod 8;

    if n8 = 0 or n8 = 3 then return 2

    elif n8 = 4 or n8 = 7 then return 4

    elif n8 = 1 then return procname((n+1)/2)

    elif n8 = 2 then return procname((n+2)/2)

    fi;

    n16:= n mod 16;

    if n16 = 5 or n16 = 14 then return 4

    elif n16 = 6 or n16 = 13 then return 6

    fi

end proc:

a007400(0):= 0: a007400(1):= 1: a007400(2):= 4:

A[1]:= 0: A[2]:= 1:

for n from 3 to 100 do

  A[n]:= A[n-1]*a007400(n-1)+A[n-2];

od:

seq(A[n], n=1..100); # Robert Israel, Jun 14 2016

PROG

(PARI) a(n)=component(component(contfracpnqn(contfrac(sum(k=0, 20, 1/2^(2^k)), n)), 1), 1)

CROSSREFS

Cf. A007400, A007404, A073415.

Sequence in context: A149164 A238420 A302179 * A085110 A013459 A041229

Adjacent sequences:  A073411 A073412 A073413 * A073415 A073416 A073417

KEYWORD

easy,frac,nonn

AUTHOR

Benoit Cloitre, Aug 23 2002

STATUS

approved

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)