A238489 Numbers k such that k+x+y is a square, where x and y are the two squares nearest to k.
0, 4, 11, 23, 56, 80, 103, 135, 204, 248, 339, 395, 444, 508, 576, 635, 711, 860, 948, 1119, 1219, 1304, 1412, 1619, 1739, 1968, 2100, 2211, 2351, 2495, 2616, 2768, 3055, 3219, 3528, 3704, 3851, 4035, 4223, 4380, 4576, 4943, 5151, 5540, 5760, 5943, 6171, 6596, 6836, 7283
Offset: 1
Keywords
Examples
The two squares nearest to 4 are 1 and 4. Because 4+1+4=9 is a square, 4 is in the sequence. The two squares nearest to 11 are 9 and 16. Because 11+9+16=36 is a square, 11 is in the sequence.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..500
Programs
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Mathematica
kxyQ[n_]:=Module[{c=Floor[Sqrt[n]]},IntegerQ[Sqrt[n+Total[Nearest[Range[c-2, c+2]^2,n,2]]]]]; Join[{0},Select[Range[3,7500],kxyQ]] (* Harvey P. Dale, Apr 24 2022 *) -
Python
# use version >= 3.8 from math import isqrt for k in range(7777): s = isqrt(k) if s*s==k: s-=1 kxy = k + 2*s*(s+1) + 1 # k + s^2 + (s+1)^2 r = isqrt(kxy) if r*r==kxy: print(str(k), end=',') -
Sage
def gen_a(): n = 1 while True: for t in range(n*n + 1, n*n + 2*n + 2): if is_square(t + 2*(n*n + n) + 1): yield t n += 1 # Ralf Stephan, Mar 09 2014
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