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