A323388 a(n) = b(n+1)/b(n) - 1 where b(1)=3 and b(k) = b(k-1) + lcm(floor(sqrt(3)*k), b(k-1)).

1, 5, 1, 1, 5, 1, 13, 5, 17, 19, 1, 11, 1, 5, 1, 29, 31, 1, 17, 1, 19, 13, 41, 43, 1, 23, 1, 1, 17, 53, 1, 19, 29, 1, 31, 1, 13, 67, 23, 71, 1, 37, 1, 1, 79, 1, 83, 1, 43, 1, 1, 13, 31, 1, 1, 1, 1, 1, 103, 1, 107, 109, 1, 1, 1, 29, 1, 1, 1, 61, 1, 1

Offset

1,2

Comments

Conjectures:

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

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

3. At the first appearance of each prime of the form floor(sqrt(3)*m), it is larger than any prime that has already appeared.

The 2nd and 3rd conjectures are proved at the Mathematics Stack Exchange link. - Sungjin Kim, Jul 17 2019

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

Mathematics Stack Exchange, Generating primes of the form floor(sqrt(3)*n)

Prog

(PARI) Generator(n)={b1=3; list=[]; for(k=2, n, b2=b1+lcm(floor(sqrt(3)*k), b1); a=b2/b1-1; list=concat(list, a); b1=b2); print(list)}
(PARI) lista(nn)={my(b1=3, b2, va=vector(nn)); for(k=2, nn+1, b2=b1+lcm(sqrtint(3*k^2), b1); va[k-1]=b2/b1-1; b1=b2); va}; \\ Michel Marcus, Aug 20 2022

Crossrefs

Cf. A184796 (primes of the form floor(sqrt(3)*m)).

Cf. A135506, A323359, A323386.

Sequence in context: A010333 A378898 A131777 * A260877 A353305 A237888

Adjacent sequences: A323385 A323386 A323387 * A323389 A323390 A323391

Keyword

nonn

Author

Pedja Terzic, Jan 13 2019

Status

approved