|
%I #5 Apr 20 2017 15:22:28
%S 1,1,1,1,5,1,1,1,13,11,1,5,5,7,1,1,1,5,7,1,1,11,1,7,5,7,1,1,23,1,11,1,
%T 19,5,13,1,1,1,5,5,5,29,19,1,1,5,1,1,37,5,5,17,11,13,25,13,5,41,7,1,5,
%U 1,25,7,5,7,1,1,5,11,11,5,5,5,5,11,5,1,11,7
%N a(n) is the smallest positive integer that makes a(n)*A007694(n)+1 a prime number, while a(n) and A007694(n) are coprimes.
%C All terms are elements of A007310, which are free of prime factor 2 and 3, since if a(n) has a factor of 2, 2*A007694(n) is also an element of A007694. Ditto for a(n) is divisible by 3 cases.
%H Lei Zhou, <a href="/A285486/b285486.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 1, A007694(1) = 1, testing k*2-1 for k in set {1, 5, 7, 11, 13, 17, 19... }, we find that 1*1 + 1 = 2 is the first prime number found. So a(1) = 1;
%e In the similar way, 1*A007694(2) + 1 = 1*2 + 1 = 3 is the first prime number found for n = 2, so a(2) = 1.
%e ...
%e For n = 5, A007694(5) = 8, 5*8 + 1 = 41 is the smallest prime found, so a(5) = 5.
%t b = 2; a = {1, b}; sp = {1}; r = {b}; While[Length[sp] < 79, f = 0;
%t While[f++; (fc = FactorInteger[f];
%t MemberQ[{2, 3}, fc[[1, 1]]]) || (! PrimeQ[f*a[[Length[a]]] + 1])];
%t AppendTo[sp, f]; c = r*2; d = r*3; e = Sort[Union[c, d]]; i = 1;
%t While[e[[i]] <= a[[Length[a]]], i++]; AppendTo[a, e[[i]]];
%t AppendTo[r, e[[i]]];
%t While[(3*r[[1]]) < r[[Length[r]]], r = Delete[r, 1]]]; sp
%Y Cf. A003586, A007310, A007694, A285483.
%K nonn,easy
%O 1,5
%A _Lei Zhou_, Apr 19 2017
|
