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%I #41 Nov 02 2022 23:14:51
%S 2,3,5,7,13,17,31,37,71,73,79,97,107,149,157,167,179,347,359,389,701,
%T 709,739,743,751,761,769,907,937,941,953,967,971,983,1069,1097,1237,
%U 1249,1259,1279,1283,1409,1429,1439,1453,1487,1523,1583,1597,1657,1723,1753
%N "Norep emirps": primes with distinct digits which remain prime when reversed.
%C There are no 10-digit terms because their sum of digits would be 45 and thus the number would be divisible by 3.
%C 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.
%H Nathaniel Johnston, <a href="/A046732/b046732.txt">Table of n, a(n) for n = 1..25332</a> (full sequence).
%H Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?curio_id=&number_id=&rank=&short=987653201">987653201</a>, Prime Curios!.
%H Martin Gardner, <a href="https://www.jstor.org/stable/24966473">Patterns in primes are a clue to the strong law of small numbers</a>, Mathematical Games, Scientific American, Vol. 243, No. 4, September, 1980.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_059.htm">Puzzle 59. Six and the nine digits primes (by Jud McCranie)</a>, The Prime Puzzles and Problems Connection.
%p 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
%t Select[Prime[Range[280]], Length[Union[x = IntegerDigits[#]]] == Length[x] && PrimeQ[FromDigits[Reverse[x]]] &] (* _Jayanta Basu_, Jun 28 2013 *)
%o (Python)
%o from sympy import prime, isprime
%o 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
%Y Intersection of A007500 and A029743.
%Y Cf. A006567, A003684, A007628, A048051, A048052, A048053, A048054, A048895.
%K easy,nonn,fini,full,base
%O 1,1
%A _Enoch Haga_
%E More terms from _Jud McCranie_.
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