A281001 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.

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

Offset: 2

Author

Felix Fröhlich, Jan 12 2017

Keywords

• nonn
• tabl

Comments

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.

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.

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.

Examples

			Array starts
   1093,    2, 1093,    2, 1093,    2, ...
     11,   71,    3,   11,   71,    3, ...
   1093,    2, 1093,    2, 1093,    2, ...
      2, 1093,    2, 1093,    2, 1093, ...
  66161,    2, 1093,    2, 1093,    2, ...
      5,    2, 1093,    2, 1093,    2, ...
  ....
		

Crossrefs

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

Programs

PARI

smallestwieftobase(n) = forprime(p=1, , if(Mod(n, p^2)^(p-1)==1, return(p)))
table(rows, cols) = for(x=2, rows+1, my(i=0, w=smallestwieftobase(x)); while(i < cols, print1(w, ", "); w=smallestwieftobase(w); i++); print(""))
table(7, 5) \\ print initial 5 terms of upper 7 rows of array