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Search: id:A096436
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| A096436 |
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a(n) = the number of squared primes and 1's needed to sum to n. |
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+0
4
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| 1, 2, 3, 1, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 2, 3, 4, 4, 3, 4, 5, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 3, 4, 5, 5, 4, 5, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 3, 4, 5, 5, 4, 5, 6, 2, 3, 4, 5, 3, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 4, 5, 6, 6, 5, 6, 2, 3, 4, 5, 3, 4, 5, 6
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) has a new maximum at n=1,2,3,7,24,73,266,795.
I suspect that a(n) <= 9 for all n. - Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 18 2004
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EXAMPLE
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a(5) = 2 because 5=4+1.
a(17) = 3 because 17=9+4+4.
A number may have many such sums: 27=25+1+1=9+9+9, 50=25+25=49+1.
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MATHEMATICA
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f[n_] := Block[{d = n, k = PrimePi[ Sqrt[n]], sp = {}}, While[d > 3, While[p = Prime[k]; d >= p^2, AppendTo[sp, p]; d = d - p^2]; k-- ]; While[d != 0, AppendTo[sp, 1]; d = d - 1]; If[Position[sp, 3] != {} && sp[[ -3]] == 1, sp = Delete[Drop[sp, -3], Position[sp, 3][[1]]]; AppendTo[sp, {2, 2, 2}]]; Reverse[ Sort[ Flatten[ sp]]]]; Table[ Length[ f[n]], {n, 105}] (from Robert G. Wilson v Sep 20 2004)
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CROSSREFS
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Cf. A001248, A002828, A045698, A051034, A063274.
Sequence in context: A063274 A002828 A098066 this_sequence A053610 A104246 A007720
Adjacent sequences: A096433 A096434 A096435 this_sequence A096437 A096438 A096439
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KEYWORD
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nonn,easy
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AUTHOR
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Tom Raes (tommy1729(AT)hotmail.com), Aug 10 2004
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 18 2004
Edited by Don Reble (djr(AT)nk.ca), Apr 23 2006
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