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A353601
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Square array read by downward antidiagonals: A(n, 1) = A185103(n) and A(n, k) = A185103(A(n, k-1)) for k > 1.
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0
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5, 7, 8, 18, 65, 17, 325, 99, 38, 7, 1432, 485, 1445, 18, 37, 2050625, 5357, 27493, 325, 18, 18, 1299108307, 12807125, 9077774, 1432, 325, 325, 65
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OFFSET
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2,1
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COMMENTS
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What is the asymptotic behavior of the rows of the array? Do all rows increase without bound, or do some rows enter a cycle?
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LINKS
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EXAMPLE
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Array starts as follows:
5, 7, 18, 325, 1432, ...
8, 65, 99, 485, 5357, ...
17, 38, 1445, 27493, 9077774, ...
7, 18, 325, 1432, 2050625, ...
37, 18, 325, 1432, 2050625, ...
...
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PROG
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(PARI) a185103(n) = for(b=2, oo, if(Mod(b, n^2)^(n-1)==1, return(b)))
a(n, k) = if(k==1, return(a185103(n)), return(a185103(a(n, k-1))))
array(rows, cols) = for(x=2, rows+1, for(y=1, cols, print1(a(x, y), ", ")); print(""))
array(5, 5) \\ Print initial 5 rows and 5 columns of array
(Python)
from functools import lru_cache
k, n2 = 2, n*n
while pow(k, n-1, n2) != 1: k += 1
return k
@lru_cache()
def T(n, k):
def auptodiag(maxd):
return [T(d+2-j, j) for d in range(1, maxd+1) for j in range(d, 0, -1)]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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