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A061051
Smallest square of the form [n digits][same n digits][further digits].
1
0, 225, 40401, 2042041, 317231721, 16198161984, 3921203921209, 400000040000001, 23391004233910041, 1100298301100298304, 141162631214116263129, 1322314049613223140496, 3171326702963171326702969, 107786983188610778698318864, 29726516052320297265160523209, 1003781781031081003781781031081
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
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
Cf. A086982.
Sequence in context: A192934 A264194 A339693 * A036428 A183822 A260864
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