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A240623 Prime numbers n such that replacing each digit d in the decimal expansion of n with d^d produces a prime. Zeros are allowed with the convention 0^0 = 1. 1
11, 13, 17, 31, 53, 61, 71, 79, 151, 167, 229, 233, 251, 263, 311, 313, 331, 337, 349, 367, 389, 409, 419, 443, 673, 751, 947, 971, 991, 1433, 1531, 1699, 1733, 1993, 2011, 2027, 2053, 2063, 2081, 2111, 2141, 2153, 2221, 2333, 2393, 2503, 2521, 2833, 2963 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

263 is in the sequence because 263 becomes 44665627 which is also prime, where 44665627 is the concatenation of the numbers (2^2, 6^6, 3^3) = (4, 46656, 27).

2503 is in the sequence because 2503 becomes 43125127 which is also prime, where 43125127 is the concatenation of the numbers (2^2, 5^5, 0^0, 3^3) = (4, 3125, 1, 27).

MAPLE

with(numtheory):T:=array(1..10):L:=array(1..10):

   for n from 1 to 1000 do:

     p:=ithprime(n):k:=0:s:=0:j:=0:

     x:=convert(p, base, 10):n1:=nops(x):

       for m from n1 by -1 to 1 do:

       k:=k+1:T[k]:=x[k]^x[k]:L[k]:=length(T[k]):

       od:

       n2:=sum('L[j]', 'j'=1..n1):s2:=0:

         for u from n1 by -1 to 1 do:

         s2:=s2+T[u]*10^(n2-L[u]):n2:=n2-L[u]:

         od:

            if type(s2, prime)=true

            then

            printf(`%d, `, p):

            else

            fi:

     od:

CROSSREFS

Cf. A068492, A240624.

Sequence in context: A162237 A325870 A090236 * A240624 A032502 A209871

Adjacent sequences:  A240620 A240621 A240622 * A240624 A240625 A240626

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Apr 09 2014

STATUS

approved

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Last modified June 30 09:10 EDT 2022. Contains 354920 sequences. (Running on oeis4.)