A204504 A204512(n)^2 = floor[A055872(n)/8]: Squares such that appending some digit in base 8 yields another square.

0, 0, 0, 1, 4, 36, 144, 1225, 4900, 41616, 166464, 1413721, 5654884, 48024900, 192099600, 1631432881, 6525731524, 55420693056, 221682772224, 1882672131025, 7530688524100, 63955431761796, 255821727047184, 2172602007770041, 8690408031080164, 73804512832419600

Offset: 1

Author

M. F. Hasler, Jan 15 2012

Keywords

• nonn
• base

Comments

Base-8 analog of A202303.

Crossrefs

See also A031149=sqrt(A023110) (base 10), A204502=sqrt(A204503) (base 9),

A204514=sqrt(A055872) (base 8), A204516=sqrt(A055859) (base 7),

A204518=sqrt(A055851) (base 6), A204520=sqrt(A055812) (base 5),

A004275=sqrt(A055808) (base 4), A001075=sqrt(A055793) (base 3),

A001541=sqrt(A055792) (base 2).

Programs

PARI

b=8;for(n=1,2e9,issquare(n^2\b) & print1((n^2\b)","))

PARI

a(n)=polcoeff(x^4*(1 + 4*x + x^2 + 4*x^3)/(1 - 35*x^2 + 35*x^4 - x^6+O(x^n)), n)

Formula

a(n)=A204512(n)^2.

G.f. = x^4*(1 + 4*x + x^2 + 4*x^3)/(1 - 35*x^2 + 35*x^4 - x^6)