A347313 Index of prime(n) in A347113, or -1 if that prime never appears.

8, 11, 7, 20, 28, 19, 37, 51, 53, 47, 101, 116, 58, 63, 99, 81, 136, 146, 159, 153, 115, 213, 176, 197, 302, 151, 215, 223, 169, 230, 276, 274, 255, 188, 233, 318, 440, 341, 347, 359, 369, 282, 386, 396, 405, 520, 638, 460, 472, 698, 357, 492, 507, 514, 529, 535, 558, 702

Offset: 1

Author

N. J. A. Sloane, Sep 06 2021

Keywords

• nonn

Comments

Conjecture: every prime appears in A347113 (every number, in fact).

The graph shows three three strong lines (and many other points). Can the primes on the three lines be described in a simple way?

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A347113.

Programs

Python

from math import gcd
from sympy import prime
def A347313(n):
    p = prime(n)
    i, j, nset, m = 1, 2, {1}, 2
    while True:
        k = m
        i += 1
        while k == j or gcd(k,j) == 1 or k in nset:
            k += 1
        if k == p:
            return i
        j = k+1
        nset.add(k)
        while m in nset:
            m += 1 # Chai Wah Wu, Sep 06 2021