A089163 Second prime factor of x = 3^p - 2^p when p is prime and omega(x) >= 2.

71, 331, 29927, 745181, 2002867877, 50642213021, 32309, 1196347, 303168989, 203778431, 17685389279, 111998979662707645844109121, 645845309, 146309, 499, 706132008101135602203621405289, 59813046375181769306016700165290169537, 1016611, 28463, 128621, 2381120538437

Offset

1,1

Comments

All prime factors of 3^p - 2^p, where p is prime, are = 1 (mod p).

Links

Amiram Eldar, Table of n, a(n) for n = 1..93

Chris Caldwell, Mersenne Primes: History, Theorems and Lists.

Example

3^11 - 2^11 = 23*331. The second prime factor is 331. These factors are congruent to 1 mod 11.

Prog

(PARI) apmapm1(a, b, n, d) = { c=0; forprime(x=2, n, c++; y = a^x-b^x; f=factor(y); v=component(f, 1); ln = length(v); if(ln>=d, print(v[d]", ")); ) }

Crossrefs

Cf. A001047.

Sequence in context: A142143 A142739 A142227 * A343913 A142375 A215470

Adjacent sequences: A089160 A089161 A089162 * A089164 A089165 A089166

Keyword

nonn

Author

Cino Hilliard, Dec 06 2003

Extensions

Name corrected by Michel Marcus, Dec 16 2022

a(18)-a(21) from Amiram Eldar, Jun 30 2023

Status

approved