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A082844 Start with 3,2 and apply the rule a(a(1)+a(2)+...+a(n)) = a(n), fill in any undefined terms with a(t) = 2 if a(t-1) = 3 and a(t) = 3 if a(t-1) = 2. 3
3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(1)=3, a(2)=2, a(a(1)+a(2)+...+a(n)) = a(n) and a(a(1)+a(2)+...+a(n)+1) = 5-a(n).

More generally, sequence a(n) = floor(r*(n+2))-floor(r*(n+1)), r = (1/2) *(z+sqrt(z^2+4)), z integer >=1, is defined with a(1), a(2) and a(a(1)+a(2)+...+a(n)+f(z)) = a(n); a(a(1)+a(2)+...+a(n)+f(z)+1) = (2z+1)-a(n) where f(1)=0, f(z)=z-2 for z>=2.

LINKS

Table of n, a(n) for n=1..105.

FORMULA

a(n) = floor(r*(n+2))-floor(r*(n+1)) where r=1+sqrt(2).

Conjecture: a(n) = A097509(n+1). - Benedict W. J. Irwin, Mar 13 2016

MAPLE

A082844:=n->floor((1+sqrt(2))*(n+2))-floor((1+sqrt(2))*(n+1)): seq(A082844(n), n=1..100); # Wesley Ivan Hurt, Mar 13 2016

MATHEMATICA

With[{r=1+Sqrt[2]}, Table[Floor[r*(n+2)]-Floor[r*(n+1)], {n, 110}]] (* Harvey P. Dale, Oct 10 2012 *)

PROG

(MAGMA) [Floor((1+Sqrt(2))*(n+2))-Floor((1+Sqrt(2))*(n+1)) : n in [1..100]]; // Wesley Ivan Hurt, Mar 13 2016

CROSSREFS

Cf. A082389, A082845, A097509.

Sequence in context: A064654 A162229 A056564 * A279124 A101406 A245219

Adjacent sequences:  A082841 A082842 A082843 * A082845 A082846 A082847

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Apr 15 2003; revised Jun 07 2003

STATUS

approved

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Last modified November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)