A193095 Number of times n can be written as concatenation of exactly two nonzero squares in decimal representation.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Reinhard Zumkeller, Jul 17 2011

Keywords

• nonn
• base

Comments

a(A193096(n))=0; a(A191933(n))>0; a(A193097(n))=1; a(A192993(n))>1; a(A038670(n))=2.

Examples

			a(164) = 2, A191933(15) = A192993(1) = 164: 1'64 == 16'4.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A010052.

Programs

Haskell

a193095 n = sum $ map c [1..(length $ show n) - 1] where
   c k | head ys == '0' = 0
       | otherwise      = a010052 (read xs) * a010052 (read ys) where
       (xs,ys) = splitAt k $ show n

PARI

A193095(n) = sum( t=1,#Str(n)-1, apply(issquare,divrem(n,10^t))==[1,1]~ && n%10^t>=10^(t-1))  \\ M. F. Hasler, Jul 24 2011

PARI

A193095(n)={ my(c,p=1); while( n>p*=10, n%p*10>=p||next; issquare(n%p)||next; issquare(n\p) && c++);c}  \\ M. F. Hasler, Jul 24 2011