cp's OEIS Frontend

A061051 Smallest square of the form [n digits][same n digits][further digits].

%I A061051 #32 Mar 27 2020 02:11:37
%S A061051 0,225,40401,2042041,317231721,16198161984,3921203921209,
%T A061051 400000040000001,23391004233910041,1100298301100298304,
%U A061051 141162631214116263129,1322314049613223140496,3171326702963171326702969,107786983188610778698318864,29726516052320297265160523209,1003781781031081003781781031081
%N A061051 Smallest square of the form [n digits][same n digits][further digits].
%C A061051 a(n) <= (2*10^n+1)^2. This bound is tight for n = 2, 7. Are there other values of n for which this bound is tight? For n = 11, there are no [further digits] block, i.e. the smallest square has 2n digits. This is true for all n in A086982. For instance, a(21) = 183673469387755102041183673469387755102041, a(33) = 132231404958677685950413223140496132231404958677685950413223140496. - _Chai Wah Wu_, Mar 25 2020
%H A061051 Chai Wah Wu, <a href="/A061051/b061051.txt">Table of n, a(n) for n = 0..37</a>
%e A061051 40401 is the first square to have the first two digits the same as the next two digits
%o A061051 (Python)
%o A061051 from sympy import integer_nthroot
%o A061051 def A061051(n):
%o A061051     if n == 0:
%o A061051         return 0
%o A061051     nstart = 10**(n-1)
%o A061051     nend = 10*nstart
%o A061051     for i in range(nstart,nend):
%o A061051         k = int(str(i)*2)
%o A061051         if integer_nthroot(k,2)[1]:
%o A061051             return k
%o A061051     for i in range(nstart,nend):
%o A061051         si = str(i)*2
%o A061051         for sj in '014569':
%o A061051             k = int(si+sj)
%o A061051             if integer_nthroot(k,2)[1]:
%o A061051                 return k # _Chai Wah Wu_, Mar 25 2020
%Y A061051 Cf. A086982.
%K A061051 base,nonn
%O A061051 0,2
%A A061051 _Erich Friedman_, May 26 2001
%E A061051 One more term from _Vladeta Jovovic_, Jun 02 2001
%E A061051 a(7)-a(15) from _Chai Wah Wu_, Mar 25 2020