A004214 Positive numbers that are not the sum of three nonzero squares. (Formerly M0959)

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

Offset

1,2

Comments

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, Nov 23 2006

A025427(a(n)) = 0. - Reinhard Zumkeller, Feb 26 2015

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

David S. Bettes, Letter to N. J. A. Sloane, Nov 05 1976.

Index entries for sequences related to sums of squares

Example

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.

Maple

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:

Mathematica

f[n_] := Flatten[Position[Take[Rest[CoefficientList[Sum[x^(i^2), {i, n}]^3, x]], n^2], 0]]; f[16] (* Ray Chandler, Dec 06 2006 *)

Prog

(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, Nov 23 2006
(Haskell)
a004214 n = a004214_list !! (n-1)
a004214_list = filter ((== 0) . a025427) [1..]
-- Reinhard Zumkeller, Feb 26 2015

Crossrefs

Cf. A000408, A025427.

Sequence in context: A027902 A067076 A060686 * A258376 A358353 A353919

Adjacent sequences: A004211 A004212 A004213 * A004215 A004216 A004217

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Apr 20 2001

Name clarified by Wolfdieter Lang, Apr 04 2013

Status

approved