

A204503


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


20



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
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OFFSET

1,3


COMMENTS

Or: Squares which remain squares when their last base9 digit is dropped.
(For the first three terms, which have only 1 digit in base 9, dropping that digit is meant to yield zero.)
Base9 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*(n4)^2 for n>5. G.f.: x^2*(7*x^612*x^511*x^4x1) / (x1)^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: A226076 A272711 A018228 * A138858 A076967 A233247
Adjacent sequences: A204500 A204501 A204502 * A204504 A204505 A204506


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jan 15 2012


STATUS

approved



