A204516 Numbers such that floor(a(n)^2 / 7) is a square.

0, 1, 2, 3, 8, 16, 45, 127, 254, 717, 2024, 4048, 11427, 32257, 64514, 182115, 514088, 1028176, 2902413, 8193151, 16386302, 46256493, 130576328, 261152656, 737201475, 2081028097, 4162056194, 11748967107, 33165873224, 66331746448

Offset: 1

Author

M. F. Hasler, Jan 15 2012

Keywords

• nonn
• easy

Comments

Or: Numbers whose square, with its last base-7 digit dropped, is again a square (where for the first 3 terms, dropping the digit is meant to yield zero).

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012
• Index to sequences related to truncating digits of squares.
• Index entries for linear recurrences with constant coefficients, signature (0,0,16,0,0,-1).

Crossrefs

Cf. A031149 (base 10), A204502 (base 9), A204514 (base 8), A204518 (base 6), A004275=sqrt(A055808) (base 4), A001075=sqrt(A055793) (base 3), A001541=sqrt(A055792) (base 2).

Programs

Mathematica

LinearRecurrence[{0,0,16,0,0,-1},{0,1,2,3,8,16,45},30] (* or *) CoefficientList[Series[ (x+2x^2+3x^3-8x^4-16x^5-3x^6)/(1-16x^3+x^6),{x,0,30}],x] (* Harvey P. Dale, Apr 22 2023 *)

PARI

b=7;for(n=0,2e9,issquare(n^2\b) & print1(n","))

Formula

G.f. = (x + 2*x^2 + 3*x^3 - 8*x^4 - 16*x^5 - 3*x^6 )/(1 - 16*x^3 + x^6).

floor(a(n)^2 / 7) = A204517(n)^2.