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Lexicographically earliest permutation of the primes such that successive absolute differences yield a permutation of all nonprime numbers.
2

%I #18 Jun 10 2016 00:20:59

%S 2,3,13,47,197,11,29,443,397,1321,4831,15559,211,5,19,41,293,113,971,

%T 419,2687,1087,1709,5851,23629,83,17341,65171,268969,20753,690607,

%U 4273,1289,81931,56267,3025961,6343,41927,1455241,14255011,21557,733,44351,7

%N Lexicographically earliest permutation of the primes such that successive absolute differences yield a permutation of all nonprime numbers.

%C It is only conjectured that this sequence is a permutation of the primes and that the successive differences yield all composite integers. The definition is rather to be understood as "The next term is chosen as the smallest prime not occurring earlier such that the successive absolute differences only yield 1 or composite numbers, and none of these occurs twice." - _M. F. Hasler_, Jan 09 2012

%H J.-M. Falcoz, <a href="/A203985/b203985.txt">Table of n, a(n) for n = 1..70</a>

%H E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/PrimeArray.htm">An array of naturals</a>, Jan 07 2012

%H E. Angelini, <a href="/A203985/a203985.pdf">An array of naturals</a> [Cached copy, with permission]

%o (PARI) {extend_first_row(a=[],u=[])=u||for(i=1,#a,u=setunion(u,Set(a[i]));forstep(j=i-1,1,-1,u=setunion(u,Set(a[j]=abs(a[j]-a[j+1])))));for(t=1,9e9,isprime(t)||next;setsearch(u,t)&&next;my(tt=t,new=Set(t));forstep(j=#a,1,-1,setsearch(u,tt=abs(tt-a[j]))&&next(2);isprime(tt)&&next(2);setsearch(new,tt)&&next(2);new=setunion(new,Set(tt)));return(t))} \\ _M. F. Hasler_, Jan 09 2012

%K nonn

%O 1,1

%A _Eric Angelini_, Jan 07 2012

%E First 70 terms computed by _Jean-Marc Falcoz_, Jan 09 2012