A128783 Numbers whose square is a nontrivial concatenation of other squares.
7, 10, 12, 13, 19, 20, 21, 30, 35, 37, 38, 40, 41, 44, 50, 57, 60, 65, 70, 80, 90, 95, 97, 100, 102, 105, 107, 108, 110, 112, 119, 120, 121, 125, 129, 130, 138, 140, 150, 160, 170, 180, 190, 191, 200, 201, 204, 205, 209, 210, 212, 220, 223, 230, 240, 250
Offset: 1
Examples
13 is included because 13^2 = 169, which includes 16 and 9, two perfect squares.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
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Haskell
a128783 n = a128783_list !! (n-1) a128783_list = filter (f . show . (^ 2)) [1..] where f zs = g (init $ tail $ inits zs) (tail $ init $ tails zs) g (xs:xss) (ys:yss) | a010052 (read xs) == 1 = a010052 (read ys) == 1 || f ys || g xss yss | otherwise = g xss yss g = False -- Reinhard Zumkeller, Oct 11 2011 -
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 for r in range(251) if ok(r*r, 1)]) # Michael S. Branicky, Jul 10 2021
Extensions
Missing terms 205 and 209 inserted by Reinhard Zumkeller, Oct 11 2011
Comments