A204503 Squares n^2 such that floor(n^2/9) is again a square.

0, 1, 4, 9, 16, 36, 81, 144, 225, 324, 441, 576, 729, 900, 1089, 1296, 1521, 1764, 2025, 2304, 2601, 2916, 3249, 3600, 3969, 4356, 4761, 5184, 5625, 6084, 6561, 7056, 7569, 8100, 8649, 9216, 9801, 10404, 11025, 11664, 12321, 12996, 13689, 14400, 15129, 15876

Offset: 1

Author

M. F. Hasler, Jan 15 2012

Keywords

• nonn
• base

Comments

Or: Squares which remain squares when their last base-9 digit is dropped.

(For the first three terms, which have only 1 digit in base 9, dropping that digit is meant to yield zero.)

Base-9 analog of A055792 (base 2), A055793 (base 3), A055808 (base 4), A055812 (base 5), A055851 (base 6), A055859 (base 7), A055872(base 8) and A023110 (base 10).

Links

• M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012
• Index to sequences related to truncating digits of squares.

Programs

Mathematica

Select[Range[0,200]^2,IntegerQ[Sqrt[Floor[#/9]]]&] (* Harvey P. Dale, Jan 27 2012 *)

PARI

b=9;for(n=1,200,issquare(n^2\b) & print1(n^2,","))

Formula

a(n) = A204502(n)^2.

Conjectures: a(n) = 9*(n-4)^2 for n>5. G.f.: x^2*(7*x^6-12*x^5-11*x^4-x-1) / (x-1)^3. - Colin Barker, Sep 15 2014