A323359 a(n) = b(n+1)/b(n) - 1 where b(1)=2 and b(k) = b(k-1) + lcm(floor(sqrt(k^3)), b(k-1)).

1, 5, 1, 11, 7, 1, 11, 1, 31, 1, 41, 23, 13, 29, 1, 1, 19, 41, 89, 1, 103, 11, 1, 1, 11, 1, 37, 1, 41, 43, 181, 1, 1, 23, 1, 1, 1, 1, 1, 131, 17, 281, 97, 43, 311, 23, 83, 1, 353, 1, 17, 1, 1, 37, 419, 43, 1, 151, 29, 17, 61, 1, 1, 131, 67, 137, 1, 191, 1, 1, 61, 89

Offset: 1

Author

Pedja Terzic, Jan 12 2019

Keywords

• nonn

Comments

Conjectures:

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

2. Every odd prime of the form floor(sqrt(m^3)) is a term of this sequence.

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

Record values appear to be A291139(m), m > 1. - Bill McEachen, Jun 23 2023

Crossrefs

Cf. A135506, A008578, A323386, A323388, A291139.

Programs

PARI

Generator(n)={b1=2;list=[]; for(k=2, n, b2=b1+lcm(sqrtint(k^3),b1); a=b2/b1-1; list=concat(list,a);b1=b2); return(list)}