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A023110
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Squares which remain squares when the last digit is removed.
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30
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0, 1, 4, 9, 16, 49, 169, 256, 361, 1444, 3249, 18496, 64009, 237169, 364816, 519841, 2079364, 4678569, 26666896, 92294449, 341991049, 526060096, 749609641, 2998438564, 6746486769, 38453641216, 133088524969, 493150849009, 758578289296, 1080936581761
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OFFSET
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1,3
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COMMENTS
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This A023110 = A031149^2 is the base 10 version of A001541^2 = A055792 (base 2), A001075^2 = A055793 (base 3), A004275^2 = A055808 (base 4), A204520^2 = A055812 (base 5), A204518^2 = A055851 (base 6), A204516^2 = A055859 (base 7), A204514^2 = A055872 (base 8) and A204502^2 = A204503 (base 9). - M. F. Hasler, Sep 28 2014
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REFERENCES
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R. K. Guy, Neg and Reg, preprint, Jan 2012.
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LINKS
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Dmitry Petukhov, Table of n, a(n) for n = 1..67 [Terms 1 to 38 by David W. Wilson; terms 39 to 40 by Robert G. Wilson v, Jan 16 2012; terms 41 to 67 by Dmitry Petukhov, Feb 12 2016]
M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012
Index to sequences related to truncating digits of squares.
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FORMULA
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Appears to satisfy a(n)=1444*a(n-7)+a(n-14)-76*sqrt(a(n-7)*a(n-14)) for n >= 16. For n = 15, 14, 13, ... this would require a(1) = 16, a(0) = 49, a(-1) = 169, ... - Henry Bottomley, May 08 2001
a(n) = A031149(n)^2. - M. F. Hasler, Sep 28 2014
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MAPLE
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count:= 1: A[1]:= 0:
for n from 0 while count < 35 do
for t in [1, 4, 6, 9] do
if issqr(10*n^2+t) then
count:= count+1;
A[count]:= 10*n^2+t;
fi
od
od:
seq(A[i], i=1..count); # Robert Israel, Sep 28 2014
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MATHEMATICA
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fQ[n_] := IntegerQ@ Sqrt@ Quotient[n^2, 10]; Select[ Range@ 1000000, fQ]^2 (* Robert G. Wilson v, Jan 15 2011 *)
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PROG
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(PARI) for(n=0, 1e7, issquare(n^2\10) & print1(n^2", ")) \\ M. F. Hasler, Jan 16 2012
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CROSSREFS
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Cf. A023111.
Cf. A031150, A053784, A031149, A055792, A055793, A055808, A055812, A055851, A055859, A055872.
Cf. A001541, A001075, A004275, A204520, A204518, A204516, A204514, A204502, A204503.
Sequence in context: A059931 A027382 A164840 * A277699 A073723 A161493
Adjacent sequences: A023107 A023108 A023109 * A023111 A023112 A023113
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KEYWORD
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nonn,base
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AUTHOR
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David W. Wilson
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EXTENSIONS
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More terms by M. F. Hasler, Jan 16 2012
Henry Bottomley's comment edited by Robert Israel, Sep 28 2014
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STATUS
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approved
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