

A323388


a(n) = b(n+1)/b(n)  1 where b(1)=3 and b(k) = b(k1) + lcm(floor(sqrt(3)*k), b(k1)).


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
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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/b11; 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



