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A246560 Least number k such that k concatenated with n is a square, or 0 if no such k exists. 1

%I #11 Sep 03 2014 23:47:57

%S 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,

%T 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,

%U 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

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

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

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

%o (PARI)

%o b(n)=v=[];for(k=10^(n-1),10^n,v=concat(v,k^2%10^n));v=vecsort(v,,8);v

%o w=[];for(k=1,250,d=digits(k);if(vecsearch(b(#d),k),w=concat(w,k)));w=vecsort(w,,8);w;

%o 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))

%o vector(200,n,a(n))

%Y Cf. A000290, A071176, A246448.

%K nonn,base

%O 1,1

%A _Derek Orr_, Aug 29 2014

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Last modified April 25 03:15 EDT 2024. Contains 371964 sequences. (Running on oeis4.)