OFFSET
1,8
COMMENTS
It is conjectured that for every n such exponent exists.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..100
FORMULA
a(n) = Min{x; reversed(prime(n)^x) is a prime}.
EXAMPLE
a(n)=1 means that rev(prime(n)) is prime i.e. prime(n) is in A007500;
a(n)=2 means that rev(prime(n)^2) is prime but rev(prime(n)) is not, like n=8:p=19 and 91 is not a prime but rev[19^2]=rev[361]=163 is a prime;
For n, the first k exponent providing rev(prime(n)^k) prime can be quite large, like at n=87: rev(p(87)^723)=rev(449^723) is the first [probably] prime has 1918 decimal digits: 948......573.
MAPLE
a:= proc(n) local k, p; p:= ithprime(n); for k while not isprime((s->
parse(cat(seq(s[-i], i=1..length(s)))))(""||(p^k))) do od; k
end:
seq(a(n), n=1..50); # Alois P. Heinz, Sep 04 2019
MATHEMATICA
a[n_] := Block[{k = 1}, While[! PrimeQ@ FromDigits@ Reverse@ IntegerDigits[ Prime[n]^k], k++]; k]; Array[a, 87] (* Giovanni Resta, Sep 04 2019 *)
PROG
(PARI) a(n) = {my(x=1, p=prime(n)); while (!ispseudoprime(fromdigits(Vecrev(digits(p^x)))), x++); x; } \\ Michel Marcus, Sep 04 2019
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Labos Elemer, Jun 24 2003
STATUS
approved