OFFSET
1,1
COMMENTS
Differs from A142159 in that 79, 2731, 8191, ... are not in this sequence.
Includes the two known Wieferich primes 1093 and 3511 (cf. A001220).
Is this a supersequence of A001220, i.e., are all Wieferich primes in the sequence?
Is p-1 always divisible by 78 = 2 * 3 * 13?
For the initial primes p in this sequence, p-1 has some interesting digit patterns in various bases, as illustrated in the following table:
p | b | base-b expansion of p-1
--------------------------------------
157 | 5 | 1111
313 | 5 | 2222
547 | 3 | 202020
547 | 4 | 20202
547 | 5 | 4141
547 | 9 | 666
547 | 16 | 222
859 | 2 | 1101011010
937 | 3 | 1021200 (nearly palindromic)
937 | 4 | 32220 (nearly palindromic)
937 | 5 | 12221
1093 | 2 | 10001000100 (periodic)
1093 | 3 | 1111110 (nearly palindromic/repdigit)
1093 | 4 | 101010
1093 | 5 | 13332 (nearly palindromic)
1093 | 16 | 444
1171 | 2 | 10010010010 (periodic)
1171 | 5 | 14140 (nearly palindromic and periodic)
1171 | 8 | 2222
1249 | 3 | 1201020 (nearly palindromic)
1249 | 5 | 14443 (nearly palindromic)
1327 | 5 | 20301 (nearly palindromic)
EXAMPLE
(2^(157-1)-1)/157 is divisible by 3 * 7 * 79 * 2731 * 8191 * 121369 * 22366891, so 157 is a term of the sequence.
PROG
(PARI) fq(n) = (2^(n-1)-1)/n
my(prd=3*7*79*2731*8191*121369*22366891); forprime(p=1, , if(Mod(fq(p), prd)==0, print1(p, ", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Jul 18 2021
STATUS
approved