

A064672


a(0) = 0, a(1) = 1; for a(n), n >= 2, write n = x^2 + y with y >= 0 as small as possible, then a(n) = a(x) + a(y).


2



0, 1, 2, 3, 2, 3, 4, 5, 4, 3, 4, 5, 6, 5, 6, 7, 2, 3, 4, 5, 4, 5, 6, 7, 6, 3, 4, 5, 6, 5, 6, 7, 8, 7, 6, 7, 4, 5, 6, 7, 6, 7, 8, 9, 8, 7, 8, 9, 10, 5, 6, 7, 8, 7, 8, 9, 10, 9, 8, 9, 10, 11, 10, 11, 4, 5, 6, 7, 6, 7, 8, 9, 8, 7, 8, 9, 10, 9, 10, 11, 6, 3, 4, 5, 6, 5, 6, 7, 8, 7, 6, 7, 8, 9, 8, 9, 10, 5, 6
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OFFSET

0,3


COMMENTS

Because of the definition of a(n), a(n^2) = a(n) and more generally a(n^(2m)) = a(n), so the sequence recursively contains itself.
a(A064689(n)) = n and a(m) < n for m < A064689(n).


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000


FORMULA

For n > 1: a(n) = a(A000196(n)) + a(A053186(n)), a(0) = 0, a(1) = 1. [Reinhard Zumkeller, Apr 27 2012]


EXAMPLE

a(7) = 5 because 7 = 2^2 + 3, a(2) = 2 and a(3) = 3, giving 5


MATHEMATICA

a[0]=0; a[1]=1; a[n_] := a[n] = a[ Floor[ Sqrt[n] ] ] + a[ n  Floor[ Sqrt[n] ]^2 ]; Table[a[n], {n, 0, 98}] (* JeanFrançois Alcover, May 23 2012, after Reinhard Zumkeller *)


PROG

(Haskell)
a064672 n = a064672_list !! n
a064672_list = 0 : 1 : f (drop 2 a000196_list) 1 1 (tail a064672_list)
where f (r:rs) r' u (v:vs)
 r == r' = (u + v) : f rs r u vs
 r /= r' = u' : f rs r u' (tail a064672_list)
where u' = a064672 $ fromInteger r
 Reinhard Zumkeller, Apr 27 2012


CROSSREFS

Cf. A064689.
Cf. A048760.
Sequence in context: A309236 A071933 A209802 * A138554 A063772 A209302
Adjacent sequences: A064669 A064670 A064671 * A064673 A064674 A064675


KEYWORD

nonn,easy,nice


AUTHOR

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 09 2001


STATUS

approved



