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A061051
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Smallest square of the form [n digits][same n digits][further digits].
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1
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0, 225, 40401, 2042041, 317231721, 16198161984, 3921203921209, 400000040000001, 23391004233910041, 1100298301100298304, 141162631214116263129, 1322314049613223140496, 3171326702963171326702969, 107786983188610778698318864, 29726516052320297265160523209, 1003781781031081003781781031081
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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40401 is the first square to have the first two digits the same as the next two digits
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PROG
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(Python)
from sympy import integer_nthroot
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]:
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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