A249162 Square array A(p, b) read by antidiagonals in which rows are indexed by successive prime numbers p_i and row b(p_i) gives the smallest prime base b_n to which q = (p_i, b_(n-1)) is a Wieferich prime.

2, 5, 3, 7, 17, 5, 19, 131, 7, 7, 127, 659, 19, 19, 11, 911, 503, 127, 127, 3, 13, 7331, 9833, 911, 911, 17, 19, 17, 167149, 49603, 7331, 7331, 131, 127, 131, 19, 387749, 327317, 167149, 167149, 659, 911, 659, 127, 23, 17153317, 13900147, 387749, 387749, 503

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

A(6,4) = 911, since the 6th prime is 13 and the smallest prime Wieferich base for 13 is 19. Applying this procedure recursively to the resulting bases a total of b-1 = 3 times leads to 911.
Array starts:
  2    5    7   19    127    911     7331   167149    387749  17153317 ...
  3   17  131  659    503   9833    49603   327317  13900147 144229223 ...
  5    7   19  127    911   7331   167149   387749  17153317       ...
  7   19  127  911   7331 167149   387749 17153317 432383657       ...
  11   3   17  131    659    503     9833    49603    327317       ...
  13  19  127  911   7331 167149   387749      ...
  17 131  659  503   9833  49603   327317      ...
  19 127  911 7331 167149 387749 17153317      ...
  23 263   79   31    229    503      ...
  29  41  313 1499    941  12011      ...
  ...

Prog

(PARI) forprime(p=1, 30, b=1; i=0; q=p; print1(p, ", "); while(i < 6, b++; if(Mod(b, q^2)^(q-1)==1 && isprime(b), print1(b, ", "); q=b; b=1; i++)); print(""))

Crossrefs

Cf. A001220, A244249.

Second column of table is A125636.

Sequence in context: A354688 A084334 A096878 * A134563 A192178 A201914

Adjacent sequences: A249159 A249160 A249161 * A249163 A249164 A249165

Keyword

nonn,tabl

Author

Felix Fröhlich, Oct 22 2014

Status

approved