A286816 Smallest b such that the k consecutive primes starting with prime(n) are all base-b Wieferich primes, i.e., satisfy b^(p-1) == 1 (mod p^2). Square array A(n, k), read by antidiagonals downwards.

5, 17, 8, 449, 26, 7, 557, 226, 18, 18, 19601, 1207, 1207, 148, 3, 132857, 54568, 1451, 606, 239, 19

Offset

1,1

Comments

Array starts

5, 17, 449, 557, 19601, 132857

8, 26, 226, 1207, 54568, 2006776

7, 18, 1207, 1451, 13543, 296449

18, 148, 606, 13543, 296449, 17134811

3, 239, 3469, 24675, 3414284, 36763941

19, 249, 653, 39016, 14380864, 34998229

Links

Table of n, a(n) for n=1..21.

Example

The sequence of base-226 Wieferich primes starts 3, 5, 7, 97, 157, ... Since 226 is the smallest b such that the three consecutive primes starting with prime(2) = 3 are base-b Wieferich primes, A(2, 3) = 226.

Prog

(PARI) primevec(initialp, vecsize) = my(v=[initialp]); while(#v < vecsize, v=concat(v, nextprime(v[#v]+1))); v
a(n, k) = my(v=primevec(prime(n), k), b=2, i=0); while(1, for(x=1, #v, if(Mod(b, v[x]^2)^(v[x]-1)!=1, i++; break)); if(i==0, return(b)); b++; i=0)
array(rows, cols) = for(s=1, rows, for(t=1, cols, print1(a(s, t), ", ")); print(""))
array(5, 6) \\ print 5 X 6 array

Crossrefs

Cf. A256236, A258787.

Sequence in context: A125636 A355658 A156323 * A276831 A180024 A356403

Adjacent sequences: A286813 A286814 A286815 * A286817 A286818 A286819

Keyword

nonn,tabl,more

Author

Felix Fröhlich, May 27 2017

Status

approved