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A046732 "Norep emirps": primes with distinct digits which remain prime when reversed. 17
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

M. Gardner, column in Scientific American, Vol. 243, No. 4, September, 1980.

There are 25332 terms in this sequence, the last of which is 987653201, as found by Harvey P. Dale - see M. Gardner's column in Scientific American, Vol. 243, No. 6, Dec. 1980, p. 28.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..25332 (full sequence)

C. Rivera, Commentary by Jud McCranie, The Prime Puzzles and Problems Connection.

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 *)

PROG

(Python)

from sympy import prime, isprime

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

CROSSREFS

Essentially the intersection of A029743 and A006567.

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

Sequence in context: A134873 A172979 A118724 * A046703 A118722 A051026

Adjacent sequences:  A046729 A046730 A046731 * A046733 A046734 A046735

KEYWORD

easy,nonn,fini,full,base

AUTHOR

Enoch Haga

EXTENSIONS

More terms from Jud McCranie.

STATUS

approved

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Last modified June 25 11:55 EDT 2017. Contains 288710 sequences.