A203719 A204521(n)^2 = floor[A055812(n)/5]: Squares which written in base 5, with some digit appended, yield another square.

0, 0, 0, 1, 9, 16, 64, 441, 3025, 5184, 20736, 142129, 974169, 1669264, 6677056, 45765225, 313679521, 537497856, 2149991424, 14736260449, 101003831721, 173072640400, 692290561600, 4745030099481, 32522920134769, 55728852710976, 222915410843904

Offset

1,5

Comments

Base-5 analog of A202303.

Links

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

Formula

Conjecture: a(n) = 323*a(n-4)-323*a(n-8)+a(n-12) for n>13. - Colin Barker, Sep 20 2014

Empirical g.f.: -x^4*(x^9 +9*x^8 +64*x^7 +16*x^6 +118*x^5 +118*x^4 +64*x^3 +16*x^2 +9*x +1) / ((x -1)*(x +1)*(x^2 -4*x -1)*(x^2 +1)*(x^2 +4*x -1)*(x^4 +18*x^2 +1)). - Colin Barker, Sep 20 2014

Prog

(PARI) b=5; 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: A303692 A119575 A174468 * A198308 A167349 A267763

Adjacent sequences: A203716 A203717 A203718 * A203720 A203721 A203722

Keyword

nonn,base

Author

M. F. Hasler, Jan 16 2012

Extensions

More terms from Colin Barker, Sep 20 2014

Status

approved