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

1,1

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.

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A057653, A234334.

Sequence in context: A075273 A176859 A176757 * A151349 A298935 A258786

Adjacent sequences: A280962 A280963 A280964 * A280966 A280967 A280968

Keyword

nonn

Author

Emmanuel Vantieghem, Feb 27 2017

Status

approved