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 A235354 Minimal k > 1 such that the base-k representation of the n-th 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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000040, A052033, A235377, A236174, A236437. Sequence in context: A332502 A287870 A308190 * A058743 A117970 A364846 Adjacent sequences: A235351 A235352 A235353 * A235355 A235356 A235357 KEYWORD nonn,base AUTHOR Vladimir Shevelev, Jan 07 2014 EXTENSIONS More terms from Peter J. C. Moses STATUS approved

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Last modified December 5 05:01 EST 2023. Contains 367575 sequences. (Running on oeis4.)