A086042 Nontrivial numbers which are prime and yield another prime when their digits are sorted in ascending order.

31, 71, 73, 97, 101, 103, 107, 109, 131, 173, 193, 197, 271, 293, 307, 311, 317, 373, 397, 419, 439, 491, 509, 547, 571, 593, 607, 617, 647, 659, 673, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 809, 839, 907, 919, 937, 941, 947, 953, 971, 983, 991

Offset: 1

Author

Chuck Seggelin, Jul 07 2003

Keywords

• base
• nonn

Comments

Primes with digits already in ascending order (like 13 and 2357) are trivial cases and are therefore excluded.

See A211654 for the sequence including the trivial cases. - M. F. Hasler, Jul 30 2019

Examples

			a(1)=31 because an ascending sort of 31's digits yields 13 which is also prime. a(53)=1009 because an ascending sort of 1009's digits yields 19 which is also prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A086402, A086051, A211654.

Programs

Magma

[p:p in PrimesUpTo(1000)|  IsPrime(Seqint(Reverse(Sort(Intseq(p,10))))) and p ne Seqint(Reverse(Sort(Intseq(p,10)))) ]; // Marius A. Burtea, Jul 30 2019

Mathematica

paoQ[n_]:=Module[{idn=IntegerDigits[n],sidn},sidn=Sort[idn];sidn!=idn && PrimeQ[FromDigits[sidn]]] (* Harvey P. Dale, Nov 14 2011 *)

PARI

select( is_A086042(p,q=fromdigits(vecsort(digits(p))))={p>q&&isprime(q)&&isprime(p)}, [1..999]) \\ M. F. Hasler, Jul 30 2019