A200918 Successive prime factors of (3^1006003 - 3)/1006003^2.

2, 2, 2, 3, 7, 13, 19, 37, 757, 111779, 670669, 6371347, 34204069, 166437443, 310854619, 385634101, 14188652209, 42594124681, 10825536799379161, 154680726732318637

Offset

1,1

Comments

1006003 = A014127(2).

2 is the only prime that occurs to a power greater than 1.

Conjecture (*Artur Jasinski*): If another infinite sequences with good Hall's examples occurred, it would have to contain primes from this sequence as constant divisors of the whole sequence, because parts of Danilov's infinite sequence (A200216, A200217, A200218) contain divisors of (3^A014127(1) - 3)/(A014127(1)^2).

a(21) > 10^18. - Max Alekseyev, Feb 26 2020

Links

Table of n, a(n) for n=1..20.

FactorDB, Factorization of 3^1006002 - 1.

Crossrefs

Cf. A014127.

Sequence in context: A024682 A091228 A181056 * A134890 A101360 A270371

Adjacent sequences: A200915 A200916 A200917 * A200919 A200920 A200921

Keyword

nonn,fini,more

Author

Artur Jasinski, Nov 24 2011

Extensions

More terms from Sean A. Irvine, Sep 06 2012

a(19)-a(20) from Max Alekseyev, Feb 13 2020

Status

approved