|
| |
|
|
A000419
|
|
Numbers that are the sum of 3 but no fewer nonzero squares.
|
|
11
|
|
|
|
3, 6, 11, 12, 14, 19, 21, 22, 24, 27, 30, 33, 35, 38, 42, 43, 44, 46, 48, 51, 54, 56, 57, 59, 62, 66, 67, 69, 70, 75, 76, 77, 78, 83, 84, 86, 88, 91, 93, 94, 96, 99, 102, 105, 107, 108, 110, 114, 115, 118, 120, 123, 126, 129, 131, 132, 133, 134, 138, 139, 140, 141, 142
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
A002828(a(n)) = 3; A025427(a(n)) > 0. - Reinhard Zumkeller, Feb 26 2015
|
|
|
REFERENCES
|
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 311.
|
|
|
LINKS
|
Ray Chandler, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Square Number.
Index entries for sequences related to sums of squares
|
|
|
FORMULA
|
Legendre: a nonnegative integer is a sum of three (or fewer) squares iff it is not of the form 4^k m with m == 7 (mod 8).
|
|
|
MATHEMATICA
|
Select[Range[150], SquaresR[3, #]>0&&SquaresR[2, #]==0&] (* Harvey P. Dale, Nov 01 2011 *)
|
|
|
PROG
|
(Haskell)
a000419 n = a000419_list !! (n-1)
a000419_list = filter ((== 3) . a002828) [1..]
-- Reinhard Zumkeller, Feb 26 2015
(PARI) is(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]%2 && f[i, 1]%4==3, return( n/4^valuation(n, 4)%8 !=7 ))); 0 \\ Charles R Greathouse IV, Feb 07 2017
(Python)
def aupto(lim):
squares = [k*k for k in range(1, int(lim**.5)+2) if k*k <= lim]
sum2sqs = set(a+b for i, a in enumerate(squares) for b in squares[i:])
sum3sqs = set(a+b for a in sum2sqs for b in squares)
return sorted(set(range(lim+1)) & (sum3sqs - sum2sqs - set(squares)))
print(aupto(142)) # Michael S. Branicky, Mar 06 2021
|
|
|
CROSSREFS
|
Cf. A000378, A000408, A000415, A002828, A004215, A025427.
Sequence in context: A022155 A066157 A073159 * A353716 A178890 A332933
Adjacent sequences: A000416 A000417 A000418 * A000420 A000421 A000422
|
|
|
KEYWORD
|
nonn,nice,easy
|
|
|
AUTHOR
|
N. J. A. Sloane and J. H. Conway
|
|
|
EXTENSIONS
|
More terms from Arlin Anderson (starship1(AT)gmail.com)
|
|
|
STATUS
|
approved
|
| |
|
|
