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A240624
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Prime numbers n such that replacing each digit d in the decimal expansion of n with d^d produces a prime. Zeros are not allowed.
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2
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11, 13, 17, 31, 53, 61, 71, 79, 151, 167, 229, 233, 251, 263, 311, 313, 331, 337, 349, 367, 389, 419, 443, 673, 751, 947, 971, 991, 1433, 1531, 1699, 1733, 1993, 2111, 2141, 2153, 2221, 2333, 2393, 2521, 2833, 2963, 3137, 3167, 3323, 3343, 3371, 3389, 3391
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OFFSET
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1,1
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COMMENTS
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Subsequence of A240623.
If zeros are counted with the convention 0^0 = 1, we find the additional primes 409, 2011, 2027, 2053, 2063, 2081, 2503, 3037, 3061, 3067, 4093, 6029, 6079, 6203, 7001, 8011, 8101, 8807, 9043, 9403, 10103, 10141, 10211, 10321, 10513, 10663, 11003, 11027, 11503, 12037,...
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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EXAMPLE
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263 is in the sequence because 263 becomes 44665627 which is also prime, where 44665627 is the concatenation (2^2, 6^6, 3^3) = (4, 46656, 27).
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MATHEMATICA
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lst={}; f[n_]:=Block[{a=IntegerDigits[n], b="", k=1, l}, l=Length[a]; While[k<l+1, b=StringJoin[b, ToString[a[[k]]^a[[k]]]]; k++]; ToExpression[b]]; Do[If[PrimeQ[f[Prime[n]]], AppendTo[lst, Prime[n]]], {n, 1, 600}]; lst
ddQ[n_]:=Module[{idn=IntegerDigits[n]}, !MemberQ[idn, 0]&&PrimeQ[FromDigits[ Flatten[ IntegerDigits/@ (idn^idn)]]]]; Select[Prime[Range[500]], ddQ] (* Harvey P. Dale, Dec 16 2014 *)
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CROSSREFS
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Cf. A068492, A240623.
Sequence in context: A325870 A090236 A240623 * A032502 A209871 A347702
Adjacent sequences: A240621 A240622 A240623 * A240625 A240626 A240627
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KEYWORD
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nonn,base
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AUTHOR
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Michel Lagneau, Apr 09 2014
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STATUS
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approved
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