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

0,165

Comments

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

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A010052.

Sequence in context: A045701 A277156 A353798 * A011725 A346619 A037808

Adjacent sequences: A193092 A193093 A193094 * A193096 A193097 A193098

Keyword

nonn,base

Author

Reinhard Zumkeller, Jul 17 2011

Status

approved