A204573 A204519(n)^2 = floor(A055851(n)/6): Squares which written in base 6, with some digit appended, yield another square.

0, 0, 0, 1, 4, 16, 121, 400, 1600, 11881, 39204, 156816, 1164241, 3841600, 15366400, 114083761, 376437604, 1505750416, 11179044361, 36887043600, 147548174400, 1095432263641, 3614553835204, 14458215340816, 107341182792481, 354189388806400, 1416757555225600

Offset

1,5

Comments

Base-6 analog of A202303.

Links

Table of n, a(n) for n=1..27.

Formula

Conjecture: a(n) = 99*a(n-3)-99*a(n-6)+a(n-9) for n>10. - Colin Barker, Sep 20 2014

Empirical g.f.: -x^4*(x^6+16*x^5+4*x^4+22*x^3+16*x^2+4*x+1) / ((x-1)*(x^2+x+1)*(x^6-98*x^3+1)). - Colin Barker, Sep 20 2014

Prog

(PARI) b=6; for(n=0, 1e7, issquare(n^2\b) & print1(n^2\b, ", "))

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).

Sequence in context: A337040 A339200 A087335 * A358880 A306561 A226102

Adjacent sequences: A204570 A204571 A204572 * A204574 A204575 A204576

Keyword

nonn,base

Author

M. F. Hasler, Jan 16 2012

Status

approved