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

%I

%S 2,31,641,12422153,66132153133

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

%C a(4) found by _Carlos Rivera_ and confirmed to be the smallest by Paul Jobling (Paul.Jobling(AT)WhiteCross.com)

%C 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

%H C. Rivera (Ed.), <a href="http://www.primepuzzles.net/puzzles/puzz_112.htm">Puzzle 112. Automorphic primes</a>, primepuzzles.net. (Published Oct. 2000 or earlier.)

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

%o (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

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

%K base,hard,nonn

%O 0,1

%A _G. L. Honaker, Jr._, Oct 20 2000

%E a(5) from _Giovanni Resta_, Sep 15 2011

%E Definition corrected by _M. F. Hasler_, Jan 23 2013

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Last modified March 20 05:34 EDT 2019. Contains 321344 sequences. (Running on oeis4.)