A204520 Numbers such that floor(a(n)^2 / 5) is a square.

0, 1, 2, 3, 7, 9, 18, 47, 123, 161, 322, 843, 2207, 2889, 5778, 15127, 39603, 51841, 103682, 271443, 710647, 930249, 1860498, 4870847, 12752043, 16692641, 33385282

Offset: 1

Author

M. F. Hasler, Jan 15 2012

Keywords

• nonn

Comments

Also: Numbers whose square, with its last base-5 digit dropped, is again a square. (For the three initial terms whose squares have only one digit in base 5, it is then understood that this yields zero.)

Crossrefs

Cf. A031149, A055812, A204502, A204514, A204516, A204518 and A004275, A001075, A001541 for the analog in bases 10,...,6 and 4, 3, 2.

Programs

Mathematica

Select[Range[0,5*10^6],IntegerQ[Sqrt[Floor[#^2/5]]]&] (* The program generates the first 24 terms of the sequence. *) (* Harvey P. Dale, Jul 15 2025 *)

PARI

b=5;for(n=0,2e9,issquare(n^2\b) && print1(n","))

Formula

a(n) = sqrt(A055812(n)).

Empirical g.f.: -x^2*(x+1)*(3*x^6 + 4*x^5 + 14*x^4 - 5*x^3 - 2*x^2 - x-1) / ((x^4 - 4*x^2 - 1)*(x^4 + 4*x^2 - 1)). - Colin Barker, Sep 15 2014