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%I #23 Apr 22 2023 12:13:50
%S 0,1,2,3,8,16,45,127,254,717,2024,4048,11427,32257,64514,182115,
%T 514088,1028176,2902413,8193151,16386302,46256493,130576328,261152656,
%U 737201475,2081028097,4162056194,11748967107,33165873224,66331746448
%N Numbers such that floor(a(n)^2 / 7) is a square.
%C 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).
%H Harvey P. Dale, <a href="/A204516/b204516.txt">Table of n, a(n) for n = 1..1000</a>
%H M. F. Hasler, <a href="/wiki/M. F. Hasler/Truncated_squares">Truncated squares</a>, OEIS wiki, Jan 16 2012
%H <a href="/index/Sq#sqtrunc">Index to sequences related to truncating digits of squares</a>.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,16,0,0,-1).
%F G.f. = (x + 2*x^2 + 3*x^3 - 8*x^4 - 16*x^5 - 3*x^6 )/(1 - 16*x^3 + x^6).
%F floor(a(n)^2 / 7) = A204517(n)^2.
%t 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 *)
%o (PARI) b=7;for(n=0,2e9,issquare(n^2\b) & print1(n","))
%Y 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).
%K nonn
%O 1,3
%A _M. F. Hasler_, Jan 15 2012
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