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

1,1

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

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A086402, A086051, A211654.

Sequence in context: A110831 A212723 A193573 * A086051 A109309 A263242

Adjacent sequences: A086039 A086040 A086041 * A086043 A086044 A086045

Keyword

base,nonn

Author

Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 07 2003

Status

approved