|
| |
|
|
A023110
|
|
Squares which remain squares when the last digit is removed.
|
|
30
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
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
For the first 4 terms the square has only one digit. It is understood that deleting this digit yields 0. - Colin Barker, Dec 31 2017
|
|
|
REFERENCES
|
R. K. Guy, Neg and Reg, preprint, Jan 2012.
|
|
|
LINKS
|
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.
|
|
|
FORMULA
|
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
Conjectures from Colin Barker, Dec 31 2017: (Start)
G.f.: x^2*(1 + 4*x + 9*x^2 + 16*x^3 + 49*x^4 + 169*x^5 + 256*x^6 - 1082*x^7 - 4328*x^8 - 9738*x^9 - 4592*x^10 - 6698*x^11 - 6698*x^12 - 4592*x^13 + 361*x^14 + 1444*x^15 + 3249*x^16 + 256*x^17 + 169*x^18 + 49*x^19 + 16*x^20) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1 - 1442*x^7 + x^14)).
a(n) = 1443*a(n-7) - 1443*a(n-14) + a(n-21) for n>22.
(End)
|
|
|
MAPLE
|
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
|
|
|
MATHEMATICA
|
fQ[n_] := IntegerQ@ Sqrt@ Quotient[n^2, 10]; Select[ Range@ 1000000, fQ]^2 (* Robert G. Wilson v, Jan 15 2011 *)
|
|
|
PROG
|
(PARI) for(n=0, 1e7, issquare(n^2\10) & print1(n^2", ")) \\ M. F. Hasler, Jan 16 2012
|
|
|
CROSSREFS
|
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
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
David W. Wilson
|
|
|
EXTENSIONS
|
More terms from M. F. Hasler, Jan 16 2012
Henry Bottomley's comment edited by Robert Israel, Sep 28 2014
|
|
|
STATUS
|
approved
|
| |
|
|
