A033682 - OEIS

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A033682

Numbers of the form (q^2+(q+1)^2)*(r^2+(r+1)^2), q,r >= 1.

25, 65, 125, 169, 205, 305, 325, 425, 533, 565, 625, 725, 793, 905, 1025, 1105, 1325, 1469, 1525, 1565, 1681, 1825, 1885, 2105, 2125, 2353, 2405, 2501, 2725, 2825, 2873, 3065, 3425, 3445, 3485, 3625

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OFFSET

1,1

COMMENTS

All terms == 1,3,5 or 9 (mod 10). - Robert Israel, Mar 20 2018

REFERENCES

G. Tenenbaum, pp. 268ff of R. L. Graham et al., eds., Mathematics of Paul Erdős I.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

N:= 10000: # to get all terms <= N

g:= n -> n^2+(n+1)^2:

sort(convert({seq(seq(g(q)*g(r), r = 1 .. floor((sqrt(2*N/g(q)-1)-1)/2)), q=1 .. floor((sqrt(2*N/5-1)-1)/2))}, list)); # Robert Israel, Mar 20 2018

MATHEMATICA

With[{nn=30}, Select[Union[Flatten[Table[(q^2+(q+1)^2)(r^2+(r+1)^2), {q, nn}, {r, q}]]], #<=5(nn^2+(nn+1)^2)&]] (* Harvey P. Dale, Jan 28 2019 *)

CROSSREFS

Sequence in context: A039376 A043199 A043979 * A020283 A350207 A211462

Adjacent sequences: A033679 A033680 A033681 * A033683 A033684 A033685

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved