A204512 Square roots of [A055872/8]: Their square written in base 8, with some digit appended, is again a square.

0, 0, 0, 1, 2, 6, 12, 35, 70, 204, 408, 1189, 2378, 6930, 13860, 40391, 80782, 235416, 470832, 1372105, 2744210, 7997214, 15994428, 46611179, 93222358, 271669860, 543339720, 1583407981, 3166815962, 9228778026, 18457556052, 53789260175, 107578520350

Offset: 1

Author

M. F. Hasler, Jan 15 2012

Keywords

• nonn
• base

Comments

Base-8 analog of A031150. The square of the terms (= truncated squares A055872) are listed in A204504.

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

Mathematica

CoefficientList[Series[(x^4 (1+2x))/(1-6x^2+x^4),{x,0,40}],x] (* Harvey P. Dale, Nov 30 2020 *)

PARI

b=8;for(n=1,1e7,issquare(n^2\b) & print1(sqrtint(n^2\b)","))

PARI

a(n)=polcoeff((2*x^5 + x^4)/(x^4 - 6*x^2 + 1+O(x^n)),n)

Formula

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