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

1,3

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

Table of n, a(n) for n=1..46.

M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012

Index to sequences related to truncating digits of squares.

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A272711 A356880 A018228 * A138858 A076967 A233247

Adjacent sequences: A204500 A204501 A204502 * A204504 A204505 A204506

Keyword

nonn,base

Author

M. F. Hasler, Jan 15 2012

Status

approved