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%I #38 Feb 07 2019 19:30:03
%S 1,2,4,5,6,12,18,43,80,154,191,228,456,684,1633,3038,5848,7253,8658,
%T 17316,25974,62011,115364,222070,275423,328776,657552,986328,2354785,
%U 4380794,8432812,10458821,12484830,24969660,37454490
%N Appending a digit to n^2 gives another perfect square.
%C Square root of 'Squares from A023110 with last digit removed'.
%C One could include an initial '0', and even list it with multiplicity 3 or 4, since 00, 01, 04 and 09 are all perfect squares: In analogy to corresponding sequences for other bases, this sequence could be defined as sqrt(floor[A023110/10]), see A204512 [base 8], A204517 (base 7), A204519 (base 6), A204521 [base 5], A001353 [base 3], A001542 [base 2]. (For bases 4 and 9, the corresponding sequence contains all integers.) - _M. F. Hasler_, Jan 16 2012
%D R. K. Guy, Neg and Reg, preprint, Jan 2012.
%H Vincenzo Librandi, <a href="/A031150/b031150.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 Joshua Stucky, <a href="https://www.math.ksu.edu/~jstucky95/papers/Pell's%20Equation%20and%20Truncated%20Squares.pdf">Pell's Equation and Truncated Squares</a>, Number Theory Seminar, Kansas State University, Feb 19 2018.
%H <a href="/index/Sq#sqtrunc">Index to sequences related to truncating digits of squares</a>.
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,38,0,0,0,0,0,0,-1).
%F G.f.: x*(x^10+2*x^9+4*x^8+5*x^7+18*x^6+12*x^5+6*x^4+5*x^3+4*x^2+2*x+1) / (x^14-38*x^7+1). - _Colin Barker_, Jan 30 2013
%e 5^2 = 25 and 16^2 = 256, so 5 is in the sequence.
%e 115364^2 = 13308852496, 364813^2 = 133088524969.
%p for i from 1 to 150000 do if (floor(sqrt(10 * i^2 + 9)) > floor(sqrt(10 * i^2))) then print(i) end if end do;
%t CoefficientList[Series[(x^10 + 2 x^9 + 4 x^8 + 5 x^7 + 18 x^6 + 12 x^5 + 6 x^4 + 5 x^3 + 4 x^2 + 2 x + 1)/(x^14 - 38 x^7 + 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 19 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,38,0,0,0,0,0,0,-1},{1,2,4,5,6,12,18,43,80,154,191,228,456,684},40] (* _Harvey P. Dale_, Jun 09 2017 *)
%Y Cf. A023110, A030686, A030687, A053784.
%Y See A202303 for the resulting squares.
%K nonn,base,easy
%O 1,2
%A _Patrick De Geest_
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