

A235354


Minimal k > 1 such that the basek representation of the nth prime, read in decimal, is also prime.


11



3, 2, 2, 4, 4, 4, 4, 4, 2, 4, 7, 4, 5, 4, 2, 4, 7, 4, 3, 4, 4, 3, 4, 2, 4, 2, 3, 4, 4, 4, 6, 4, 8, 3, 2, 4, 2, 2, 4, 2, 2, 3, 4, 3, 4, 2, 3, 8, 4, 2, 4, 7, 4, 4, 8, 10, 10, 9, 3, 5, 3, 4, 3, 4, 2, 4, 2, 6, 10, 3, 7, 4, 2, 3, 2, 2, 4, 10, 4, 3, 4, 3, 10, 3, 3
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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.


LINKS



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)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



