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

%I A347313 #26 Sep 08 2021 08:10:30
%S A347313 8,11,7,20,28,19,37,51,53,47,101,116,58,63,99,81,136,146,159,153,115,
%T A347313 213,176,197,302,151,215,223,169,230,276,274,255,188,233,318,440,341,
%U A347313 347,359,369,282,386,396,405,520,638,460,472,698,357,492,507,514,529,535,558,702
%N A347313 Index of prime(n) in A347113, or -1 if that prime never appears.
%C A347313 Conjecture: every prime appears in A347113 (every number, in fact).
%C A347313 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 A347313 Alois P. Heinz, <a href="/A347313/b347313.txt">Table of n, a(n) for n = 1..10000</a>
%o A347313 (Python)
%o A347313 from math import gcd
%o A347313 from sympy import prime
%o A347313 def A347313(n):
%o A347313     p = prime(n)
%o A347313     i, j, nset, m = 1, 2, {1}, 2
%o A347313     while True:
%o A347313         k = m
%o A347313         i += 1
%o A347313         while k == j or gcd(k,j) == 1 or k in nset:
%o A347313             k += 1
%o A347313         if k == p:
%o A347313             return i
%o A347313         j = k+1
%o A347313         nset.add(k)
%o A347313         while m in nset:
%o A347313             m += 1 # _Chai Wah Wu_, Sep 06 2021
%Y A347313 Cf. A347113.
%K A347313 nonn
%O A347313 1,1
%A A347313 _N. J. A. Sloane_, Sep 06 2021