A087552 a(1) = 1, then the smallest prime divisor of A065447(n) not included earlier.

1, 2, 11, 5, 3, 29, 101, 113, 41, 271, 7, 13, 239, 613, 73, 137, 37, 8291, 9091, 157637, 313, 21649, 9901, 2733970560857, 53, 79, 229, 4649, 31, 13001, 17, 19, 6529, 664193, 6781, 52579, 1111111111111111111

Offset

1,2

Comments

Conjecture: Every prime is a member and this is a rearrangement of the noncomposite numbers.

Proof of conjecture: primes 2=a(1) and 5=a(3) are terms, while any other prime divides infinitely many numbers of the form A002275([(n+1)/2]) = (10^[(n+1)/2]-1)/9, which in turn divide A065447(n). Thus every prime will sooner or later appear as a(n). - Max Alekseyev, Jul 03 2019

Links

Table of n, a(n) for n=1..37.

Example

a(6) = 29; smallest prime divisor of 100111000011111000000 not included earlier is 29. The prime divisors are 2, 3, 5, 29, 37, 97 and 106872959.

Crossrefs

Cf. A002275, A065447.

Sequence in context: A257112 A077272 A009301 * A124688 A339807 A158616

Adjacent sequences: A087549 A087550 A087551 * A087553 A087554 A087555

Keyword

base,more,nonn

Author

Amarnath Murthy, Sep 13 2003

Extensions

More terms from David Wasserman, Jun 06 2005

Offset corrected by Max Alekseyev, Jul 03 2019

Status

approved