A229140 - OEIS

A229140

Smallest k such that k^2 + l^2 = n-th number expressible as sum of two squares (A001481).

0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 3, 2, 0, 1, 2, 4, 3, 0, 1, 2, 4, 3, 0, 1, 4, 2, 3, 5, 0, 1, 2, 6, 3, 5, 4, 0, 1, 2, 5, 3, 4, 7, 0, 1, 2, 5, 3, 7, 4, 6, 0, 1, 2, 8, 3, 6, 4, 0, 1, 5, 2, 7, 3, 6, 4, 9, 8, 0, 1, 2, 3, 6, 9, 4, 7, 5, 0, 1, 2, 9, 3, 8, 4, 7, 5, 0

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OFFSET

1,6

COMMENTS

Conjecture: the values between two zeros are always distinct from each other.

LINKS

Zhuorui He, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 0 if A001481(n) is square.

From Zhuorui He, Jul 08 2025 and Sep 20 2025: (Start)

a(n) = sqrt(A001481(n)-A385236(n)^2).

a(n) = A328803(n) - A385236(n).

a(n) = A064875(A001481(n)). (End)

EXAMPLE

The 6th number expressible as sum of two squares A001481(6) = 8 = 2^2 + 2^2, so a(6)=2.

PROG

(PARI) for(n=0, 300, my(s=sqrtint(n)); forstep(i=s, 0, -1, if(issquare(n-i*i), print1(sqrtint(n-i*i), ", "); break))); \\ shift corrected by Michel Marcus, Jul 08 2025

CROSSREFS

Cf. A001481, A064875, A385236 (largest k), A385237, A328803, A283303, A283304.

Sequence in context: A025842 A141100 A270655 * A280317 A283304 A058685

Adjacent sequences: A229137 A229138 A229139 * A229141 A229142 A229143

KEYWORD

nonn

AUTHOR

Ralf Stephan, Sep 15 2013

STATUS

approved