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

2, 31, 641, 12422153, 66132153133

Offset

0,1

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

Links

Table of n, a(n) for n=0..4.

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A108491 A088104 A362860 * A058244 A245051 A024235

Adjacent sequences: A057689 A057690 A057691 * A057693 A057694 A057695

Keyword

base,hard,nonn

Author

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

Extensions

a(5) from Giovanni Resta, Sep 15 2011

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

Status

approved