A096783 Numbers n such that n, n+1, n+2, n+3, n+4 are all of the form x^2+2*y^2 for nonnegative x, y.

0, 96, 800, 2400, 3200, 3648, 4096, 4800, 6272, 7296, 9600, 18272, 19648, 20000, 20672, 23648, 28224, 28800, 29472, 31424, 34848, 36896, 37472, 43072, 48672, 50272, 51200, 53600, 53824, 55072, 57696, 59648, 62848, 64800, 66048, 69824, 76896, 79200, 82048, 84672, 85600, 87648, 89472, 96448, 98400

Offset

1,2

Comments

All terms are divisible by 32. - Robert Israel, Jul 02 2026

Links

Robert Israel, Table of n, a(n) for n = 1..6922

Example

96=8^2+2*4^2, 97=5^2+2*6^2, 98 = 0^2+2*7^2,99=9^2+2*3^2=7^2+2*5^2,100=10^2+2*0^2

Maple

N:= 10^6: # for terms <= N
Q:= {seq(seq(x^2 + 2*y^2, y=0..floor(sqrt((N-x^2)/2))), x=0..floor(sqrt(N)))}:
sort(convert(Q intersect (Q -~ 1) intersect (Q -~ 2) intersect (Q -~3) intersect(Q -~ 4), list)); # Robert Israel, Jul 02 2026

Mathematica

f[n_] := f[n_] = Block[{y = 0}, While[x = Sqrt[n - 2y^2]; !IntegerQ[x] && x >= 0, y++ ]; If[x \[Element] Reals, 1, 0]]; Select[ Range[0, 76895], f[ # ] == f[ # + 1] == f[ # + 2] == f[ # + 3] == f[ # + 4] == 1 &] (* Robert G. Wilson v, Aug 20 2004 *)

Crossrefs

Sequence in context: A269032 A187610 A269215 * A253410 A326576 A202890

Adjacent sequences: A096780 A096781 A096782 * A096784 A096785 A096786

Keyword

nonn,changed

Author

John L. Drost, Aug 16 2004

Extensions

More terms from Robert G. Wilson v, Aug 20 2004

More terms from Robert Israel, Jul 02 2026

Status

approved