A134641 Prime permutational numbers A134640.

2, 5, 7, 11, 19

Offset: 1

Author

Artur Jasinski, Nov 05 2007

Keywords

• nonn
• fini
• full

Comments

Conjecture: This sequence is finite and complete.

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

Crossrefs

Cf. A134640.

Programs

Mathematica

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*)

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