A244529 Prime numbers whose decimal expansion contains no repeated digits or zeros, whose digits cannot be rearranged to form another prime number.

2, 3, 5, 7, 19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 257, 263, 269, 431, 487, 523, 541, 827, 829, 853, 859, 2861, 5623, 5849

Offset

1,1

Comments

There are only thirty prime numbers which meet the criteria.

The largest prime in this sequence happens, as noted by Farideh Firoozbakht, to have the property pi(5849) = (pi(5)*pi(8)*pi(4)*pi(9)) * (pi(pi(5))*pi(pi(8))*pi(pi(4))*pi(pi(9))), where pi = A000720. Note that 5849 is the earliest multi-digit prime with this property. - Jonathan Vos Post, Jun 30 2014

Links

Table of n, a(n) for n=1..30.

Prime Curios, 5849

Example

541 (prime) -> 145, 154, 415, 451, 514 (all nonprime).

Maple

with(combinat):
T:= n-> sort(map(h-> h[], select(z-> nops(z)=1,
    map(x-> map(y-> select(isprime, parse(cat(y[]))),
    permute(x)), choose([$1..9], n)))))[]:
seq(T(n), n=1..4);  # Alois P. Heinz, Jun 29 2014

Mathematica

nrdQ[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 0]&&Length[Union[idn]] == Length[idn]&&Count[FromDigits/@Permutations[idn], _?PrimeQ]==1]; Select[ Prime[ Range[800]], nrdQ] (* Harvey P. Dale, Apr 27 2018 *)

Crossrefs

Cf. A000720.

Sequence in context: A153590 A360041 A360040 * A332583 A345335 A025019

Adjacent sequences: A244526 A244527 A244528 * A244530 A244531 A244532

Keyword

nonn,base,fini,full

Author

Andreas Boe, Jun 29 2014

Status

approved