id:A053610 - OEIS Search Results

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Number of positive squares needed to sum to n using the greedy algorithm.

+0
2

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)

	OFFSET	`1,2`
	COMMENT	`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.`
	FORMULA	`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`
	EXAMPLE	`7=4+1+1+1, so 7 requires 4 squares using the greedy algorithm, so a(7)=4.`
	MATHEMATICA	`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}]`
	CROSSREFS	`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`
	KEYWORD	`nonn`
	AUTHOR	`Jud McCranie (j.mccranie(AT)comcast.net), Mar 19 2000`

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Last modified July 4 18:25 EDT 2008. Contains 140886 sequences.

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