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Search: id:A004214
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| A004214 |
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Numbers that are not the sum of three nonzero squares.
(Formerly M0959)
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+0
6
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| 1, 2, 4, 5, 7, 8, 10, 13, 15, 16, 20, 23, 25, 28, 31, 32, 37, 39, 40, 47, 52, 55, 58, 60, 63, 64, 71, 79, 80, 85, 87, 92, 95, 100, 103, 111, 112, 119, 124, 127, 128, 130, 135, 143, 148, 151, 156, 159, 160, 167, 175, 183, 188, 191, 199, 207, 208, 215, 220, 223, 231
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Not of the form x^2 + y^2 + z^2 with x, y, z >=1.
Complement of A000408, but skipping the zero. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2006
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Ray Chandler, Table of n, a(n) for n=1..10000
Index entries for sequences related to sums of squares
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EXAMPLE
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The smallest numbers that are the sums of 3 nonzero squares are 3=1+1+1, 6=1+1+4, 9=1+4+4, etc.
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MAPLE
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gf := sum(sum(sum(q^(x^2+y^2+z^2), x=1..25), y=1..25), z=1..25): s := series(gf, q, 500): for n from 1 to 500 do if coeff(s, q, n)=0 then printf(`%d, `, n) fi:od:
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MATHEMATICA
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f[n_] := Flatten[Position[Take[Rest[CoefficientList[Sum[x^(i^2), {i, n}]^3, x]], n^2], 0]]; f[16] (*Chandler*)
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PROGRAM
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(PARI) isA000408(n)={ local(a, b) ; a=1; while(a^2+1<n, b=1 ; while(b<=a && a^2+b^2<n, if(issquare(n-a^2-b^2), return(1) ) ; b++ ; ) ; a++ ; ) ; return(0) ; } isA004214(n)={ return(! isA000408(n)) ; } { n=1 ; for(an=1, 20000, if(isA004214(an), print(n, " ", an) ; n++ ; ) ; ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2006
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CROSSREFS
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Cf. A000408.
Sequence in context: A027902 A067076 A060686 this_sequence A072013 A123064 A108513
Adjacent sequences: A004211 A004212 A004213 this_sequence A004215 A004216 A004217
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 20 2001
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