A353601 Square array read by downward antidiagonals: A(n, 1) = A185103(n) and A(n, k) = A185103(A(n, k-1)) for k > 1.

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

Offset: 2

Author

Felix Fröhlich, Apr 29 2022

Keywords

• nonn
• tabl
• more

Comments

What is the asymptotic behavior of the rows of the array? Do all rows increase without bound, or do some rows enter a cycle?

Examples

			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, ...
...
		

Crossrefs

Cf. A185103.

Programs

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
def A185103(n):
    k, n2 = 2, n*n
    while pow(k, n-1, n2) != 1: k += 1
    return k
@lru_cache()
def T(n, k):
    if k == 1: return A185103(n)
    return A185103(T(n, k-1))
def auptodiag(maxd):
    return [T(d+2-j, j) for d in range(1, maxd+1) for j in range(d, 0, -1)]
print(auptodiag(6)) # Michael S. Branicky, Apr 29 2022

Extensions

a(16)-a(28) from Michael S. Branicky, Apr 29 2022