A029743 Primes with distinct digits.

2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 103, 107, 109, 127, 137, 139, 149, 157, 163, 167, 173, 179, 193, 197, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 317, 347, 349, 359, 367, 379, 389

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• fini
• full
• base

Comments

This sequence has 283086 terms, the last being 987654103 = A007810(9). - Jud McCranie

Intersection of A010784 and A000040; A178788(a(n)) * A010051(a(n)) = 1. [Reinhard Zumkeller, Sep 25 2011]

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..283086, full sequence
• Patrick De Geest, World!Of Numbers

Crossrefs

Cf. A000040, A007810, A010051, A010784, A178788.

Programs

Haskell

a029743 n = a029743_list !! (n-1)
a029743_list = filter ((== 1) . a010051) a010784_list
-- Reinhard Zumkeller, Sep 25 2011

Mathematica

t={};Do[p=Prime[n];If[Select[Transpose[Tally[IntegerDigits[p]]][[2]],#>1 &]=={},AppendTo[t,p]],{n,77}];t (* Jayanta Basu, May 04 2013 *)
Select[Prime[Range[80]],Max[DigitCount[#]]<2&] (* Harvey P. Dale, Sep 13 2020 *)

Python

from sympy import isprime
from itertools import permutations as P
dist = [p for d in range(1, 11) for p in P("0123456789", d) if p[0] != "0"]
afull = [t for t in (int("".join(p)) for p in dist) if isprime(t)]
print(afull[:100]) # Michael S. Branicky, Aug 04 2022