A288097 Square array read by antidiagonals downwards: A(n, 1) = smallest base-prime(n) Wieferich prime and A(n, k) = smallest base-A(n, k-1) Wieferich prime for k > 1.

1093, 2, 11, 1093, 71, 2, 2, 3, 1093, 5, 1093, 11, 2, 2, 71, 2, 71, 1093, 1093, 3, 2, 1093, 3, 2, 2, 11, 1093, 2, 2, 11, 1093, 1093, 71, 2, 1093, 3, 1093, 71, 2, 2, 3, 1093, 2, 11, 13, 2, 3, 1093, 1093, 11, 2, 1093, 71, 2, 2, 1093, 11, 2, 2, 71, 1093, 2, 3, 1093, 1093, 7

Offset

1,1

Links

Table of n, a(n) for n=1..66.

Example

Array starts
1093,    2, 1093,    2, 1093,    2, 1093,    2, 1093,    2
  11,   71,    3,   11,   71,    3,   11,   71,    3,   11
   2, 1093,    2, 1093,    2, 1093,    2, 1093,    2, 1093
   5,    2, 1093,    2, 1093,    2, 1093,    2, 1093,    2
  71,    3,   11,   71,    3,   11,   71,    3,   11,   71
   2, 1093,    2, 1093,    2, 1093,    2, 1093,    2, 1093
   2, 1093,    2, 1093,    2, 1093,    2, 1093,    2, 1093
   3,   11,   71,    3,   11,   71,    3,   11,   71,    3
  13,    2, 1093,    2, 1093,    2, 1093,    2, 1093,    2
   2, 1093,    2, 1093,    2, 1093,    2, 1093,    2, 1093

Mathematica

f[n_] := Block[{p = 2}, While[! Divisible[n^(p - 1) - 1, p^2], p = NextPrime@ p]; p]; T[n_, k_] := T[n, k] = If[k == 1, f@ Prime@ n, f@ T[n, k - 1]]; Table[Function[n, T[n, k]][m - k + 1], {m, 12}, {k, m, 1, -1}] // Flatten (* Michael De Vlieger, Jun 06 2017 *)

Prog

(PARI) a039951(n) = forprime(p=1, , if(Mod(n, p^2)^(p-1)==1, return(p)))
table(rows, cols) = forprime(p=1, prime(rows), my(i=0, w=a039951(p)); while(i < cols, print1(w, ", "); w=a039951(w); i++); print(""))
table(10, 10) \\ print initial 10 rows and 10 columns of table

Crossrefs

Cf. A039951, A252801, A252802, A252812, A269111, A281001, A281002, A268479.

Sequence in context: A239875 A091673 A377655 * A281001 A271100 A258368

Adjacent sequences: A288094 A288095 A288096 * A288098 A288099 A288100

Keyword

nonn,tabl

Author

Felix Fröhlich, Jun 05 2017

Extensions

More terms from Michael De Vlieger, Jun 06 2017

Status

approved