A004441 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A004441

Numbers that are not the sum of 4 distinct nonzero squares.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 49, 52, 53, 55, 56, 58, 59, 60, 61, 64, 67, 68

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

It has been shown that 157 is the last odd number in this sequence. Beyond 157, the terms grow exponentially. - T. D. Noe, Apr 07 2007

Taking a(86) to a(120) as initial terms, A004441(n) satisfies the 35th-order recurrence relation u(n) = 4*u(n-35). - Ant King, Aug 13 2010

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000 (using A004195 and A004196)

Paul T. Bateman, Adolf J. Hildebrand and George B. Purdy, Sums of distinct squares, Acta Arith. 67 (1994), 349-380.

H. D. Nguyen and D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013. [Mentions this sequence.]

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4).

Index entries for sequences related to sums of squares

MATHEMATICA

data1=Reduce[w^2+x^2+y^2+z^2==# && 0<w<x<y<z<#, {w, x, y, z}, Integers]&/@Range[1000]; data2=If[Head[ # ]===And, 1, Length[ # ]] &/@data1; DeleteCases[Table[If[data2[[k]]>0, 0, k], {k, 1, Length[data2]}], 0] (* Ant King, Aug 13 2010 *)

CROSSREFS

Cf. A004195, A004196, A004433 (complement).

Sequence in context: A192218 A070915 A083243 * A004438 A109425 A357873

Adjacent sequences: A004438 A004439 A004440 * A004442 A004443 A004444

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved