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

1,1

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

Prog

(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

Crossrefs

Cf. A347113.

Sequence in context: A109596 A164801 A156925 * A077060 A123939 A134787

Adjacent sequences: A347310 A347311 A347312 * A347314 A347315 A347316

Keyword

nonn

Author

N. J. A. Sloane, Sep 06 2021

Status

approved