Consider the following code to produce the sequence $x_1,\ldots,x_{n+1}$ where $x_i=11\cdots1$ ($i$ digits 1). Is there an easier way to do this?
n = 7
X = Table[Sum[10^i, {i, 0, k - 1}], {k, 1, n + 1}]
R = Table[Mod[X[[k]], n], {k, 1, n + 1}]
X
R
Also, the code defines the list R
of remainders on division of $x_i$ by $n$. The output of R
is {1, 4, 6, 5, 2, 0, 1, 4}
.
I'd like to do the following: determine the indexes producing the first two equal elements of R
(for example, since R[[1]]=R[[7]]
I'd like to do some math with X[[1]]
and X[[7]]
).
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