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

2,1

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.

Links

Table of n, a(n) for n=2..62.

Example

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, ...
  ....

Prog

(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

Crossrefs

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

Sequence in context: A239875 A091673 A288097 * A271100 A258368 A174422

Adjacent sequences: A280998 A280999 A281000 * A281002 A281003 A281004

Keyword

nonn,tabl

Author

Felix Fröhlich, Jan 12 2017

Status

approved