A204518 Numbers such that floor(a(n)^2 / 6) is a square.

0, 1, 2, 3, 5, 10, 27, 49, 98, 267, 485, 970, 2643, 4801, 9602, 26163, 47525, 95050, 258987, 470449, 940898, 2563707, 4656965, 9313930, 25378083, 46099201, 92198402, 251217123, 456335045, 912670090, 2486793147, 4517251249, 9034502498, 24616714347

Offset: 1

Author

M. F. Hasler, Jan 15 2012

Keywords

• nonn
• easy

Comments

Or: Numbers whose square, with its last base-6 digit dropped, is again a square. (For the three initial terms whose square has only one digit in base 6, this is then meant to yield zero.)

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,10,0,0,-1).

Crossrefs

Cf. A023110 (base 10), A204502 (base 9), A204514 (base 8), A204516 (base 7), A204520 (base 5), A004275 (base 4), A055793 (base 3), A055792 (base 2).

Programs

PARI

b=6;for(n=0,2e9,issquare(n^2\b) & print1(n","))

PARI

concat(0, Vec(-x^2*(x+1)*(3*x^4+7*x^3-2*x^2-x-1)/(x^6-10*x^3+1) + O(x^100))) \\ Colin Barker, Sep 18 2014

Formula

a(n) = sqrt(A055851(n)).

From Colin Barker, Sep 18 2014: (Start)

a(n) = 10*a(n-3) - a(n-6) for n > 7.

G.f.: -x^2*(x+1)*(3*x^4 + 7*x^3 - 2*x^2 - x - 1) / (x^6-10*x^3+1). (End)

a(3n+2) = A001079(n). a(3n) = A087799(n-1). - R. J. Mathar, Feb 05 2020

Extensions

More terms from Colin Barker, Sep 18 2014