A285486 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.

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, 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, 1, 25, 7, 5, 7, 1, 1, 5, 11, 11, 5, 5, 5, 5, 11, 5, 1, 11, 7

Offset: 1

Author

Lei Zhou, Apr 19 2017

Keywords

• nonn
• easy

Comments

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.

Examples

			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;
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.
...
For n = 5, A007694(5) = 8, 5*8 + 1 = 41 is the smallest prime found, so a(5) = 5.
		

Links

• Lei Zhou, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003586, A007310, A007694, A285483.

Programs

Mathematica

b = 2; a = {1, b}; sp = {1}; r = {b}; While[Length[sp] < 79, f = 0;
While[f++; (fc = FactorInteger[f];
    MemberQ[{2, 3}, fc[[1, 1]]]) || (! PrimeQ[f*a[[Length[a]]] + 1])];
  AppendTo[sp, f]; c = r*2; d = r*3; e = Sort[Union[c, d]]; i = 1;
While[e[[i]] <= a[[Length[a]]], i++]; AppendTo[a, e[[i]]];
AppendTo[r, e[[i]]];
While[(3*r[[1]]) < r[[Length[r]]], r = Delete[r, 1]]]; sp