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A055872 a(n) and floor(a(n)/8) are both squares; i.e., squares that remain squares when written in base 8 and last digit is removed. 14

%I

%S 0,1,4,9,36,289,1156,9801,39204,332929,1331716,11309769,45239076,

%T 384199201,1536796804,13051463049,52205852196,443365544449,

%U 1773462177796,15061377048201,60245508192804

%N a(n) and floor(a(n)/8) are both squares; i.e., squares that remain squares when written in base 8 and last digit is removed.

%C For the first 3 terms which have only 1 digit in base 8, removing this digit is meant to yield 0.

%C Base-8 analog of A055792 (base 2), A055793 (base 3), A055808 (base 4), A055812 (base 5), A055851 (base 6), A055859 (base 7), A204503 (base 9) and A023110 (base 10). - _M. F. Hasler_, Jan 15 2012

%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 (0,35,0,-35,0,1)

%F a(n) = A204514(n)^2. - _M. F. Hasler_, Jan 15 2012

%F Empirical g.f.: -x^2*(4*x+1)*(9*x^4-26*x^2+1) / ((x-1)*(x+1)*(x^2-6*x+1)*(x^2+6*x+1)). - _Colin Barker_, Sep 15 2014

%e a(5) = 289 because 289 = 17^2 = 441 base 8 and 44 base 8 = 36 = 6^2.

%t Select[Range[0,8*10^6]^2,IntegerQ[Sqrt[FromDigits[Most[ IntegerDigits[ #,8]], 8]]]&] (* _Harvey P. Dale_, Aug 02 2016 *)

%o (PARI) b=8;for(n=1,200,issquare(n^2\b) && print1(n^2,",")) \\ _M. F. Hasler_, Jan 15 2012

%Y Cf. A023110, A055792 (bisection).

%K base,nonn,easy

%O 1,3

%A _Henry Bottomley_, Jul 14 2000

%E More terms added and offset changed to 1 by _M. F. Hasler_, Jan 15 2012

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Last modified April 4 04:53 EDT 2020. Contains 333212 sequences. (Running on oeis4.)