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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)). 2
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 (list; graph; refs; listen; history; text; internal format)
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 Math StackExchange link. - Sungjin Kim, Jul 17 2019

LINKS

Table of n, a(n) for n=1..72.

Math StackExchange, Generating Primes of the form  ...

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)}

CROSSREFS

Cf. A008578, A135506, A323359, A323386.

Sequence in context: A108691 A010333 A131777 * A260877 A237888 A286462

Adjacent sequences:  A323385 A323386 A323387 * A323389 A323390 A323391

KEYWORD

nonn

AUTHOR

Pedja Terzic, Jan 13 2019

STATUS

approved

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Last modified October 18 23:35 EDT 2021. Contains 348071 sequences. (Running on oeis4.)