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

1,5

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.

Links

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

Example

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.

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

Crossrefs

Cf. A003586, A007310, A007694, A285483.

Sequence in context: A091051 A183097 A353958 * A230368 A256690 A181985

Adjacent sequences: A285483 A285484 A285485 * A285487 A285488 A285489

Keyword

nonn,easy

Author

Lei Zhou, Apr 19 2017

Status

approved