A052015 Primes with distinct digits in ascending order.

2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579

Offset: 1

Author

Patrick De Geest, Nov 15 1999

Keywords

• nonn
• base
• fini
• full
• easy

Examples

			Last term is a(100) = 23456789.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..100 (complete sequence)

Crossrefs

Cf. A028864, A028867, A052014.

Programs

Maple

b:= proc(n) `if`(isprime(n), n, [][]), seq(
      b(parse(cat(n, j))), j=irem(n, 10)+1..9)
    end:
sort([seq(b(n), n=1..9)])[];  # Alois P. Heinz, Jun 16 2025

Mathematica

t={};Do[p=Prime[n];If[Select[Differences[IntegerDigits[p]],#<=0&]=={},AppendTo[t,p]],{n,380}];t (* Jayanta Basu, May 04 2013 *)
Select[Prime[Range[5000]],Min[Differences[IntegerDigits[#]]]>0&] (* Harvey P. Dale, Jun 20 2015 *)
Select[FromDigits@# &/@Subsets@Range@9,PrimeQ] (* Hans Rudolf Widmer, Apr 08 2023 *)

PARI

A052015=vecextract( vecsort( vector( 511,i,isprime( t=eval( concat( vecextract(Vec("123456789"),i ))))*t),NULL,8),"^1") /* for old PARI versions replace,NULL,8),"^1" by ),"-100.." */ \\ M. F. Hasler, Jan 27 2009

Python

from sympy import isprime
from itertools import combinations
def agen(): # generator of terms
    for d in range(1, 9):
        for c in combinations("123456789", d):
            if isprime(t:=int("".join(c))):
                yield t
print(list(agen())) # Michael S. Branicky, Dec 13 2023