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

%I A193095 #22 Jan 07 2023 09:26:55
%S A193095 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,
%T A193095 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,
%U A193095 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A193095 Number of times n can be written as concatenation of exactly two nonzero squares in decimal representation.
%C A193095 a(A193096(n))=0; a(A191933(n))>0; a(A193097(n))=1; a(A192993(n))>1; a(A038670(n))=2.
%H A193095 Reinhard Zumkeller, <a href="/A193095/b193095.txt">Table of n, a(n) for n = 0..10000</a>
%e A193095 a(164) = 2, A191933(15) = A192993(1) = 164: 1'64 == 16'4.
%o A193095 (Haskell)
%o A193095 a193095 n = sum $ map c [1..(length $ show n) - 1] where
%o A193095    c k | head ys == '0' = 0
%o A193095        | otherwise      = a010052 (read xs) * a010052 (read ys) where
%o A193095        (xs,ys) = splitAt k $ show n
%o A193095 (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
%o A193095 (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
%Y A193095 Cf. A010052.
%K A193095 nonn,base
%O A193095 0,165
%A A193095 _Reinhard Zumkeller_, Jul 17 2011