A057692 Smallest prime which produces exactly n+1 different primes after n applications of the A048376 transform.

2, 31, 641, 12422153, 66132153133

Offset: 0

Author

G. L. Honaker, Jr., Oct 20 2000

Keywords

• base
• hard
• nonn
• more

Comments

a(4) found by Carlos Rivera and confirmed to be the smallest by Paul Jobling (Paul.Jobling(AT)WhiteCross.com)

a(5) = 66132153133 leads to a final (probable) prime of 3560 digits. If zero is allowed, then a(5) = 12505785661 and the last (probable) prime would have 10982 digits. - Giovanni Resta, Sep 15 2011

Examples

			31 becomes 3331 and both 31 and 3331 are primes. 641 becomes 66666644441 and then 66666666666666666666666666666666666644444444444444441 and all 3 are primes.
		

Links

• C. Rivera (Ed.), Puzzle 112. Automorphic primes, primepuzzles.net. (Published Oct. 2000 or earlier.)

Crossrefs

a(1,2,3,...) is a subsequence of A057628.

Programs

PARI

A057692(n,s=2)={ forprime(p=s,, my(q=p); for(i=2,n, isprime(q=A048376(q))||next(2)); isprime(A048376(q))||return(p))} \\ Impractical for n>3. - M. F. Hasler, Jan 23 2013

Extensions

a(5) from Giovanni Resta, Sep 15 2011

Definition corrected by M. F. Hasler, Jan 23 2013