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

1,3

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.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Mathematica

1 / Divide @@@ Partition[FoldList[# + LCM[Floor[#2*Sqrt[2]], #] &, 2, Range[2, 100]], 2, 1] - 1 (* Paolo Xausa, Jan 08 2026 *)

Prog

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

Crossrefs

Cf. A135506, A008578, A323359, A323388.

Sequence in context: A019697 A217173 A246952 * A021179 A153613 A356706

Adjacent sequences: A323383 A323384 A323385 * A323387 A323388 A323389

Keyword

nonn,look

Author

Pedja Terzic, Jan 13 2019

Status

approved