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A019547
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Squares which are a decimal concatenation of two or more squares.
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4
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49, 100, 144, 169, 361, 400, 441, 900, 1225, 1369, 1444, 1600, 1681, 1936, 2500, 3249, 3600, 4225, 4900, 6400, 8100, 9025, 9409, 10000, 10404, 11025, 11449, 11664, 12100, 12544, 14161, 14400, 14641, 15625, 16641, 16900, 19044, 19600, 22500, 25600, 28900
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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0 counts as a square here.
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REFERENCES
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L. Widmer, Construction of Elements of the Smarandache Square-Partial-Digital Sequence, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 145-146.
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LINKS
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Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, Table of n, a(n), sqrt(a(n)), all possible decompositions of a(n) into squares for n = 1..10000 (excluding solutions with leading zeros)
Sylvester Smith, A Set of Conjectures on Smarandache Sequences, Bulletin of Pure and Applied Sciences, (Bombay, India), Vol. 15 E (No. 1), 1996, pp. 101-107.
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FORMULA
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n^2 < a(n) < 100n^2. - Charles R Greathouse IV, Sep 19 2012
a(n) = A128783(n)^2. - Michael S. Branicky, Jul 10 2021
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EXAMPLE
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1369 is a term as it can be partitioned as 1, 36 and 9. 1444 is a term as it can be partitioned as 1, 4, 4, 4. Again, 100 is 1, 0, 0.
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MATHEMATICA
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r[n_, d_] := Catch@Block[{z = Length@d, t}, z < 1 || Do[If[IntegerQ@ Sqrt@ (t = FromDigits@Take[d, i]) && t < n && r[n, Take[d, i - z]], Throw@ True], {i, z}]]; Select[Range[4, 10^4]^2, r[#, IntegerDigits@ #] &] (* Giovanni Resta, Apr 30 2013 *)
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PROG
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(Python)
from math import isqrt
def issquare(n): return isqrt(n)**2 == n
def ok(n, c):
if n%10 in { 2, 3, 7, 8}: return False
if issquare(n) and c > 1: return True
d = str(n)
for i in range(1, len(d)):
if issquare(int(d[:i])) and ok(int(d[i:]), c+1): return True
return False
print([r*r for r in range(180) if ok(r*r, 1)]) # Michael S. Branicky, Jul 10 2021
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CROSSREFS
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Cf. A010052, A000290, A128783.
Sequence in context: A161689 A354342 A230653 * A228878 A067673 A250653
Adjacent sequences: A019544 A019545 A019546 * A019548 A019549 A019550
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KEYWORD
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nonn,base
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AUTHOR
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R. Muller
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EXTENSIONS
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More terms from Christian N. K. Anderson, Apr 30 2013
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STATUS
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approved
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