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A046732
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"Norep emirps": primes with distinct digits which remain prime when reversed.
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16
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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Chris K. Caldwell and G. L. Honaker, Jr., 987653201, Prime Curios!.
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MAPLE
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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
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MATHEMATICA
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Select[Prime[Range[280]], Length[Union[x = IntegerDigits[#]]] == Length[x] && PrimeQ[FromDigits[Reverse[x]]] &] (* Jayanta Basu, Jun 28 2013 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn,fini,full,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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