A046732 "Norep emirps": primes with distinct digits which remain prime when reversed.

2, 3, 5, 7, 13, 17, 31, 37, 71, 73, 79, 97, 107, 149, 157, 167, 179, 347, 359, 389, 701, 709, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 1069, 1097, 1237, 1249, 1259, 1279, 1283, 1409, 1429, 1439, 1453, 1487, 1523, 1583, 1597, 1657, 1723, 1753

Offset: 1

Author

Enoch Haga

Keywords

• easy
• nonn
• fini
• full
• base

Comments

There are no 10-digit terms because their sum of digits would be 45 and thus the number would be divisible by 3.

There are 25332 terms in this sequence, the last of which is 987653201, as found by Harvey P. Dale. - see Martin Gardner's column in Scientific American.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..25332 (full sequence).
• Chris K. Caldwell and G. L. Honaker, Jr., 987653201, Prime Curios!.
• Martin Gardner, Patterns in primes are a clue to the strong law of small numbers, Mathematical Games, Scientific American, Vol. 243, No. 4, September, 1980.
• Carlos Rivera, Puzzle 59. Six and the nine digits primes (by Jud McCranie), The Prime Puzzles and Problems Connection.

Crossrefs

Intersection of A007500 and A029743.

Cf. A006567, A003684, A007628, A048051, A048052, A048053, A048054, A048895.

Programs

Maple

read(transforms): A046732 := proc(n) option remember: local d,k,p,distdig: if(n=1)then return 2: fi: p:=procname(n-1): do p:=nextprime(p): if(isprime(digrev(p)))then d:=convert(p,base,10): distdig:=true: for k from 0 to 9 do if(numboccur(d,k)>1)then distdig:=false: break: fi: od: if(distdig)then return p: fi: fi: od: end: seq(A046732(n),n=1..52); # Nathaniel Johnston, May 29 2011

Mathematica

Select[Prime[Range[280]], Length[Union[x = IntegerDigits[#]]] == Length[x] && PrimeQ[FromDigits[Reverse[x]]] &] (* Jayanta Basu, Jun 28 2013 *)

Python

from sympy import prime, isprime
A046732 = [p for p in (prime(n) for n in range(1,10**3)) if len(str(p)) == len(set(str(p))) and isprime(int(str(p)[::-1]))] # Chai Wah Wu, Aug 14 2014

Extensions

More terms from Jud McCranie.