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Index of prime(n) in A347113, or -1 if that prime never appears.
6

%I #26 Sep 08 2021 08:10:30

%S 8,11,7,20,28,19,37,51,53,47,101,116,58,63,99,81,136,146,159,153,115,

%T 213,176,197,302,151,215,223,169,230,276,274,255,188,233,318,440,341,

%U 347,359,369,282,386,396,405,520,638,460,472,698,357,492,507,514,529,535,558,702

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

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

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

%H Alois P. Heinz, <a href="/A347313/b347313.txt">Table of n, a(n) for n = 1..10000</a>

%o (Python)

%o from math import gcd

%o from sympy import prime

%o def A347313(n):

%o p = prime(n)

%o i, j, nset, m = 1, 2, {1}, 2

%o while True:

%o k = m

%o i += 1

%o while k == j or gcd(k,j) == 1 or k in nset:

%o k += 1

%o if k == p:

%o return i

%o j = k+1

%o nset.add(k)

%o while m in nset:

%o m += 1 # _Chai Wah Wu_, Sep 06 2021

%Y Cf. A347113.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Sep 06 2021