A385236 Largest x such that x^2+y^2 = A001481(n), x and y are nonnegative integers.

0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 3, 4, 5, 5, 5, 4, 5, 6, 6, 6, 5, 6, 7, 7, 6, 7, 7, 6, 8, 8, 8, 6, 8, 7, 8, 9, 9, 9, 8, 9, 9, 7, 10, 10, 10, 9, 10, 8, 10, 9, 11, 11, 11, 8, 11, 10, 11, 12, 12, 11, 12, 10, 12, 11, 12, 9, 10, 13, 13, 13, 13, 12, 10, 13, 12, 13, 14, 14, 14, 11, 14, 12, 14, 13, 14, 15

Offset

1,4

Comments

A229140(n) gives smallest x such that x^2+y^2 = A001481(n), x and y are nonnegative integers.

Links

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

Formula

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

a(n) = sqrt(A001481(n)-A229140(n)^2).

a(n) = A328803(n) - A229140(n).

a(n) = A064876(A001481(n)).

Example

For n=9, A001481(9)=13=2^2+3^2, so A229140(9)=2 and a(9)=3.
For n=14, A001481(14)=25=3^2+4^2=0^2+5^2, so A229140(14)=0 and a(14)=5.

Prog

(PARI) for(n=0, 300, my(s=sqrtint(n)); forstep(i=s, 0, -1, if(issquare(n-i*i), print1(i, ", "); break)))

Crossrefs

Cf. A001481, A064876, A229140, A328803, A283303, A283304.

Sequence in context: A351167 A283303 A280079 * A116513 A122651 A343378

Adjacent sequences: A385233 A385234 A385235 * A385237 A385238 A385239

Keyword

nonn,easy,look

Author

Zhuorui He, Jul 08 2025

Status

approved