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A134641 Prime permutational numbers A134640. 11

%I #7 Dec 14 2015 17:54:20

%S 2,5,7,11,19

%N Prime permutational numbers A134640.

%C Conjecture: This sequence is finite and complete.

%C The conjecture is correct: in base 2k permutational numbers are divisible by 2k-1 and in base 2k+1 permutational numbers are divisible by k. Hence it suffices to check bases up to 3. - _Charles R Greathouse IV_, Dec 14 2015

%t a = {}; b = {}; Do[AppendTo[b, n]; w =Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; If[PrimeQ[j], AppendTo[a, j]], {m, 1, Length[w]}], {n, 0, 10}]; a (*Artur Jasinski*)

%o (PARI) for(b=2,3, for(i=0,b!-1, p=fromdigits(apply(j->j-1, numtoperm(b,i)),b); if(isprime(p), print1(p", ")))) \\ _Charles R Greathouse IV_, Dec 14 2015

%Y Cf. A134640.

%K nonn,fini,full

%O 1,1

%A _Artur Jasinski_, Nov 05 2007

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