OFFSET
0,2
COMMENTS
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
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..37
EXAMPLE
40401 is the first square to have the first two digits the same as the next two digits
PROG
(Python)
from sympy import integer_nthroot
def A061051(n):
if n == 0:
return 0
nstart = 10**(n-1)
nend = 10*nstart
for i in range(nstart, nend):
k = int(str(i)*2)
if integer_nthroot(k, 2)[1]:
return k
for i in range(nstart, nend):
si = str(i)*2
for sj in '014569':
k = int(si+sj)
if integer_nthroot(k, 2)[1]:
return k # Chai Wah Wu, Mar 25 2020
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Erich Friedman, May 26 2001
EXTENSIONS
One more term from Vladeta Jovovic, Jun 02 2001
a(7)-a(15) from Chai Wah Wu, Mar 25 2020
STATUS
approved