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A240624
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.
2
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
OFFSET
1,1
COMMENTS
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,...
LINKS
EXAMPLE
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).
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A325870 A090236 A240623 * A375091 A032502 A209871
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Apr 09 2014
STATUS
approved