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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.
7
5, 17, 8, 449, 26, 7, 557, 226, 18, 18, 19601, 1207, 1207, 148, 3, 132857, 54568, 1451, 606, 239, 19, 4486949, 2006776, 13543, 13543, 3469, 249, 38, 126664001, 20950343, 296449, 296449, 24675, 653, 423, 28, 2363321449, 230695118, 23250274, 17134811, 3414284, 39016, 5649, 28, 28, 5229752849, 5229752849, 882345432, 741652533, 36763941, 14380864, 217682, 26645, 63, 14
OFFSET
1,1
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.
Array starts:
n=1: 5, 17, 449, 557, 19601, 132857
n=2: 8, 26, 226, 1207, 54568, 2006776
n=3: 7, 18, 1207, 1451, 13543, 296449
n=4: 18, 148, 606, 13543, 296449, 17134811
n=5: 3, 239, 3469, 24675, 3414284, 36763941
n=6: 19, 249, 653, 39016, 14380864, 34998229
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
Columns: A039678 (k=1), A259075 (k=2), A344827 (k=3), A344828 (k=4), A344829 (k=5), A344830 (k=6), A344831 (k=7), A344832 (k=8).
Cf. A256236 (row n=1), A258787.
Sequence in context: A125636 A355658 A156323 * A276831 A180024 A356403
KEYWORD
nonn,tabl
AUTHOR
Felix Fröhlich, May 27 2017
EXTENSIONS
More terms from Max Alekseyev, Oct 10 2023
STATUS
approved