A280965 Nonsquares whose distances to the two nearest squares are squares.

5, 8, 40, 45, 65, 80, 153, 160, 200, 221, 325, 360, 416, 425, 493, 520, 680, 725, 925, 936, 1025, 1040, 1073, 1088, 1305, 1360, 1768, 1800, 1813, 1845, 1961, 2000, 2320, 2385, 2501, 2600, 2925, 3016, 3185, 3200, 3400, 3445, 3848, 3869, 3944, 3965, 4640, 4745, 5185, 5248, 5265, 5328, 5525, 5576, 5785, 5920, 6120

Offset: 1

Author

Emmanuel Vantieghem, Feb 27 2017

Keywords

• nonn

Comments

The sequence is infinite because there are terms of it between n^2 and (n+1)^2 whenever 2n+1 is a sum of two squares.

Examples

			a(3) = 40 because the two nearest squares are 36 and 49 and 40 - 36 = 4, 49 - 40 = 9 are both squares.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A057653, A234334.

Programs

Mathematica

Select[Range[6120], IntegerQ[Sqrt[# - (Floor[Sqrt[#]])^2]] && IntegerQ[Sqrt[(Ceiling[Sqrt[#]])^2 - #]] &]

PARI

is(n)=my(k=sqrtint(n)); issquare(n-k^2) && issquare((k+1)^2-n) && n>k^2 \\ Charles R Greathouse IV, Feb 27 2017

PARI

list(lim)=my(v=List(),k2,K2,n); for(k=2,sqrtint(lim\1)-1, k2=k^2; K2=(k+1)^2; for(s=1,sqrtint(K2-k2-1), n=k2+s^2; if(issquare(K2-n), listput(v,n)))); k2=sqrtint(lim\1)^2; K2=(sqrtint(lim\1)+1)^2; for(n=k2+1,lim, if(issquare(n-k2) && issquare(K2-n), listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Feb 27 2017