A323386 a(n) = b(n+1)/b(n) - 1 where b(1)=2 and b(k) = b(k-1) + lcm(floor(sqrt(2)*k),b(k-1)).

1, 1, 5, 7, 1, 3, 11, 1, 7, 5, 1, 1, 19, 7, 11, 1, 5, 13, 1, 29, 31, 1, 11, 1, 1, 19, 13, 41, 1, 43, 1, 23, 1, 1, 1, 13, 53, 1, 1, 19, 59, 1, 31, 1, 13, 1, 67, 23, 1, 1, 73, 1, 19, 1, 79, 1, 41, 83, 1, 43, 29, 89, 1, 13, 31, 47, 1, 97, 1, 1, 101, 103

Offset: 1

Author

Pedja Terzic, Jan 13 2019

Keywords

• nonn

Comments

Conjectures:

1. This sequence consists only of 1's and primes.

2. Every odd prime of the form floor(sqrt(2)*m) is a term of this sequence.

3. At the first appearance of each prime of the form floor(sqrt(2)*m), it is the next prime after the largest prime that has already appeared.

Crossrefs

Cf. A135506, A008578, A323359, A323388.

Programs

PARI

Generator(n)={b1=2; list=[]; for(k=2, n, b2=b1+lcm(floor(sqrt(2)*k), b1); a=b2/b1-1; list=concat(list,a); b1=b2); print(list)}