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A234334 Numbers k such that both distances from k to two nearest squares are perfect squares. 5
0, 1, 5, 8, 25, 40, 45, 65, 80, 153, 160, 169, 200, 221, 325, 360, 416, 425, 493, 520, 625, 680, 725, 925, 936, 1025, 1040, 1073, 1088, 1305, 1360, 1681, 1768, 1800, 1813, 1845, 1961, 2000, 2320, 2385, 2501, 2600, 2925, 3016, 3185, 3200, 3400, 3445, 3721, 3848 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Except a(1)=0, a(n) are numbers k such that both k-x and y-k are perfect squares, where x and y are two nearest to k squares: x < k <= y.

The sequence of sums of distances begins: 1, 1, 5, 5, 9, 13, 13, 17, 17, 25, 25, 25, 29, 29, 37, 37, 41, 41, 45, 45, 49, 53, 53, 61, 61, 65, 65, 65, 65, 73, 73, 81, 85, ... (cf. A057653).

Each term is either a square or has a pair: if i^2 + j^2 = 2*m+1 then m^2+i^2 and m^2+j^2 are both in the sequence.

LINKS

Robert Israel, Table of n, a(n) for n = 1..6000

EXAMPLE

The two squares nearest to 25 are 16 and 25, because both 25-25=0 and 25-16=9 are squares, 25 is in the sequence.

The two squares nearest to 45 are 36 and 49, because both 45-36=9 and 49-45=4 are squares, 45 is in the sequence.

MAPLE

filter:= proc(n) local a;

  if issqr(n) then a:= sqrt(n)-1 else a:= floor(sqrt(n)) fi;

  issqr(n-a^2) and issqr((a+1)^2-n)

end proc:

select(filter, [$0..5000]); # Robert Israel, Jan 21 2021

CROSSREFS

Cf. A000290.

Cf. subsequences: A007204, A234335, A234336.

Cf. A234348.

Sequence in context: A140113 A166652 A286571 * A025623 A069959 A038250

Adjacent sequences:  A234331 A234332 A234333 * A234335 A234336 A234337

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, Dec 23 2013

STATUS

approved

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Last modified October 18 22:48 EDT 2021. Contains 348070 sequences. (Running on oeis4.)