A343763 Common prime factors of A007663(183)/1093 and A007663(490)/3511.

3, 7, 79, 2731, 8191, 121369, 22366891

Offset: 1

Author

Felix Fröhlich, Apr 28 2021

Keywords

• nonn
• fini
• full

Comments

The sequence is complete (cf. Michon).

Are these primes necessarily prime factors of A007663(i)/p when p = prime(i) is a Wieferich prime (A001220)?

Note the following curious observation: 3 * 7 * 79 * 2731 * 8191 * 121369 * 22366891 = 100743818301219097892181. That number is a repdigit in bases 4 and 64 and undulating in bases 2, 8, 128, 2048 and 8192. Compare that to observations from John Blythe Dobson (cf. Dobson).

Links

• J. B. Dobson, A note on the two known Wieferich primes
• Gerard P. Michon, Wieferich Primes 1093 and 3511

Crossrefs

Cf. A001220, A007663, A010785, A033619, A172290, A242715.

Programs

PARI

fq(n) = (2^(n-1)-1)/n
my(x=fq(1093)/1093, y=fq(3511)/3511); forprime(p=1, , if(Mod(x, p)==0 && Mod(y, p)==0, print1(p, ", ")))