A246560 Least number k such that k concatenated with n is a square, or 0 if no such k exists.

8, 0, 0, 6, 2, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 1, 0, 0, 3, 2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 17, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 16, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 8, 0, 0, 0, 23

Offset: 1

Author

Derek Orr, Aug 29 2014

Keywords

• nonn
• base

Comments

a(n) = 0 if and only if n is in A246448.

Examples

			The smallest square ending with 5 is 25, so a(5) = 2.
		

Crossrefs

Cf. A000290, A071176, A246448.

Programs

PARI

b(n)=v=[];for(k=10^(n-1),10^n,v=concat(v,k^2%10^n));v=vecsort(v,,8);v
w=[];for(k=1,250,d=digits(k);if(vecsearch(b(#d),k),w=concat(w,k)));w=vecsort(w,,8);w;
a(n)=if(!vecsearch(w,n),return(0));if(vecsearch(w,n),j=1;s=Str(n);while(!issquare(eval(concat(Str(j),s))),j++);return(j))
vector(200,n,a(n))