

A287218


a(n) = smallest k such that (6*k3)*2^prime(n)  1 is prime.


1



1, 1, 3, 1, 1, 2, 3, 9, 12, 8, 3, 4, 3, 1, 36, 25, 8, 12, 19, 21, 3, 12, 19, 40, 9, 14, 1, 14, 2, 18, 81, 56, 49, 38, 38, 26, 3, 33, 103, 12, 67, 12, 11, 8, 48, 79, 2, 43, 136, 82, 12, 46, 78, 31, 117, 126, 34, 4, 27, 49, 83, 3, 57, 234, 12, 10, 116, 128, 53, 13
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

For n from 1 to 2000, a(n)/prime(n) is always < 1.8.
As N increases, (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} prime(n)) tends to log(2)/3; this is consistent with the prime number theorem as the probability that x*2^n1 is prime with odd x divisible by 3 is ~ 3/(n*log(2)) and after n*log(2)/3 try (n*log(2)/3)*(3/(n*log(2)) = 1.


LINKS

Pierre CAMI, Table of n, a(n) for n = 1..2000


FORMULA

a(n) = A285808(A000040(n)).


MATHEMATICA

sk[n_]:=Module[{k=1, t=2^Prime[n]}, While[!PrimeQ[(6k3)*t1], k++]; k]; Array[ sk, 70] (* Harvey P. Dale, Nov 14 2018 *)


CROSSREFS

Subsequence of A285808.
Cf. A284325, A284631.
Sequence in context: A128316 A065836 A078712 * A306438 A221978 A035254
Adjacent sequences: A287215 A287216 A287217 * A287219 A287220 A287221


KEYWORD

nonn


AUTHOR

Pierre CAMI, May 22 2017


STATUS

approved



