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A258778 Least base b >= 2 such that prime(n) is an absolute prime in base b. 2

%I #9 Jun 16 2015 14:19:47

%S 3,2,3,2,5,3,5,5,4,4,2,7,7,6,7,4,8,8,9,6,8,9,11,7,7,9,11,11,13,10,2,

%T 10,12,11,13,17,12,11,12,9,16,9,6,13,15,10,6,11,19,12,19,13,11,16,7,

%U 17,19,19,12,7,16,19,7,10,13,19,22,7,19,19,18,18,21,10

%N Least base b >= 2 such that prime(n) is an absolute prime in base b.

%C a(n) < prime(n) for n > 1. This is true since prime(n) in base prime(n)-1 is written as 11 which is an absolute prime.

%C Conjecture: a(n) < prime(n)-1 for n > 2.

%H Chai Wah Wu, <a href="/A258778/b258778.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Permutable_prime">Permutable prime</a>

%e a(78) = 13. prime(78) = 397 in base 10 and 397_10 = 247_13. Rearranging the digits in base 13, we get 274_13 = 433_10, 427_13 = 709_10, 472_13 = 769_10, 724_13 = 1213_10, 742_13 = 1237_10, all of which are prime.

%Y Cf. A003459, A258706, A258802.

%K nonn

%O 1,1

%A _Chai Wah Wu_, Jun 11 2015

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