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Search: id:A053610
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| A053610 |
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Number of positive squares needed to sum to n using the greedy algorithm. |
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+0
2
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| 1, 2, 3, 1, 2, 3, 4, 2, 1, 2, 3, 4, 2, 3, 4, 1, 2, 3, 4, 2, 3, 4, 5, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 5, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 5, 3, 4, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 5, 3, 4, 5, 2, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 5, 3, 4, 5, 2, 3, 4, 1, 2, 3, 4
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Define f(n)= n - x2 where (x+1)^2 > n >= > x^2. a(n) = number of iterations in f(...f(f(n))...) to reach 0.
a(n) = 1 iff n is a perfect square.
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FORMULA
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a(n) = A007953(A007961(n)) - Henry Bottomley (se16(AT)btinternet.com), Jun 01 2000
a(n) = a(n-(int(sqrt(n)))^2)+1 = a(A053186(n))+1 [with a(0) = 0] - Henry Bottomley (se16(AT)btinternet.com), May 16 2000
A053610 = A002828 + A062535. [From M. F. Hasler ((AT)univ-ag.fr), Dec 04 2008]
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EXAMPLE
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7=4+1+1+1, so 7 requires 4 squares using the greedy algorithm, so a(7)=4.
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MATHEMATICA
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f[n_] := (n - Floor[Sqrt[n]]^2); g[n_] := (m = n; c = 1; While[a = f[m]; a != 0, c++; m = a]; c); Table[ g[n], {n, 1, 105}]
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PROGRAM
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(PARI) A053610(n, c=1)=while(n-=sqrtint(n)^2, c++); c [From M. F. Hasler ((AT)univ-ag.fr), Dec 04 2008]
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CROSSREFS
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Cf. A006892, A055401, A007961.
Sequence in context: A002828 A098066 A096436 this_sequence A104246 A007720 A129968
Adjacent sequences: A053607 A053608 A053609 this_sequence A053611 A053612 A053613
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KEYWORD
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nonn
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AUTHOR
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Jud McCranie (j.mccranie(AT)comcast.net), Mar 19 2000
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