login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Square array read by antidiagonals downwards: A(n, 1) = smallest Wieferich prime to base n and A(n, k) = smallest Wieferich prime to base A(n, k-1) for k > 1.
3

%I #19 Feb 03 2017 21:51:54

%S 1093,2,11,1093,71,1093,2,3,2,2,1093,11,1093,1093,66161,2,71,2,2,2,5,

%T 1093,3,1093,1093,1093,2,3,2,11,2,2,2,1093,11,2,1093,71,1093,1093,

%U 1093,2,71,1093,3,2,3,2,2,2,1093,3,2,11,71,1093,11,1093,1093,1093,2

%N Square array read by antidiagonals downwards: A(n, 1) = smallest Wieferich prime to base n and A(n, k) = smallest Wieferich prime to base A(n, k-1) for k > 1.

%C Row n becomes periodic, repeating the terms 2, 1093 if n is in A252801 when n is prime or if A039951(n) is in A252801 when n is composite.

%C Row n becomes periodic, repeating the terms 3, 11, 71 if n is in A252802 when n is prime or if A039951(n) is in A252802 when n is composite.

%C Row n becomes periodic, repeating the terms 83, 4871 if n is in A252812 when n is prime or if A039951(n) is in A252812 when n is composite.

%e Array starts

%e 1093, 2, 1093, 2, 1093, 2, ...

%e 11, 71, 3, 11, 71, 3, ...

%e 1093, 2, 1093, 2, 1093, 2, ...

%e 2, 1093, 2, 1093, 2, 1093, ...

%e 66161, 2, 1093, 2, 1093, 2, ...

%e 5, 2, 1093, 2, 1093, 2, ...

%e ....

%o (PARI) smallestwieftobase(n) = forprime(p=1, , if(Mod(n, p^2)^(p-1)==1, return(p)))

%o table(rows, cols) = for(x=2, rows+1, my(i=0, w=smallestwieftobase(x)); while(i < cols, print1(w, ", "); w=smallestwieftobase(w); i++); print(""))

%o table(7, 5) \\ print initial 5 terms of upper 7 rows of array

%Y Cf. A039951, A252801, A252802, A252812, A281002.

%K nonn,tabl

%O 2,1

%A _Felix Fröhlich_, Jan 12 2017