OFFSET
1,1
COMMENTS
Conjecture 1. Every number 2, ..., 10 occurs infinitely many times.
Conjecture 2. There exists limit of average (a(1) + ... + a(n))/n.
Conjecture: The average in Conjecture 2 exists and is equal to 10. - Charles R Greathouse IV, Jan 08 2014
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
Prime(7) = 17. The base 2 representation of 17 is 10001, which reinterpreted in decimal is 73 * 137; the base 3 representation of 17 is 122, which reread as decimal is 2 * 61; and the base 4 representation of 17 is 101, which reread as decimal is prime, so therefore a(7) = 4.
PROG
(PARI) rebase(n, from, to=10)=subst(Pol(digits(n, from)), 'x, to)
a(n)=my(p=prime(n)); for(b=2, 9, if(isprime(rebase(p, b)), return(b))); 10 \\ Charles R Greathouse IV, Jan 08 2014
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Jan 07 2014
EXTENSIONS
More terms from Peter J. C. Moses
STATUS
approved