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A019547 Squares which are a decimal concatenation of two or more squares. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

0 counts as a square here.

REFERENCES

L. Widmer, Construction of Elements of the Smarandache Square-Partial-Digital Sequence, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 145-146.

LINKS

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.

FORMULA

n^2 < a(n) < 100n^2. - Charles R Greathouse IV, Sep 19 2012

a(n) = A128783(n)^2. - Michael S. Branicky, Jul 10 2021

EXAMPLE

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.

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A010052, A000290, A128783.

Sequence in context: A161689 A354342 A230653 * A228878 A067673 A250653

Adjacent sequences: A019544 A019545 A019546 * A019548 A019549 A019550

KEYWORD

nonn,base

AUTHOR

R. Muller

EXTENSIONS

More terms from Christian N. K. Anderson, Apr 30 2013

STATUS

approved

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Last modified February 3 01:24 EST 2023. Contains 360024 sequences. (Running on oeis4.)