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A347756 Local minima in A347113.

%I A347756 #30 Sep 29 2021 10:14:47
%S A347756 1,2,3,7,11,17,19,23,31,37,59,61,67,79,97,151,157,199,211,229,271,307,
%T A347756 337,367,499,577,601,619,691,727,829,877,937,1009,1237,1279,1297,1399,
%U A347756 1459,1531,1609,1657,1867,2011,2029,2089,2131,2137,2179,2281,2311,2467,2539
%N A347756 Local minima in A347113.
%C A347756 Distinct terms in A347755.
%C A347756 Conjecture: subset of A008578.
%H A347756 Chai Wah Wu, <a href="/A347756/b347756.txt">Table of n, a(n) for n = 1..6626</a> (terms n = 1..899 from Michael De Vlieger)
%H A347756 Michael De Vlieger, <a href="/A347755/a347755.png">Log-log scatterplot of A347113(n)</a> for 1 <= n <= 2^12, showing terms in A347307 in red, those in A347755 joined in gold, and terms in this sequence in blue.
%F A347756 A347757(n) = index of a(n) in A347113.
%t A347756 Block[{nn = 2^13, a = {1}, c, k, m, u = 2, v}, v = a; Map[Set[c[#], 1] &, Union@ a]; Do[Set[k, u]; If[PrimeQ[#], m = 2; While[IntegerQ[c[m #]], m++]; k = m #, While[Or[IntegerQ[c[k]], k == #, GCD[k, #] == 1], k++]] &[a[[-1]] + 1]; AppendTo[a, k]; Set[c[k], 1]; AppendTo[v, u]; If[k == u, While[IntegerQ[c[u]], u++]], nn]; Union@ v]
%t A347756 (* or using A347113 bfile: *)
%t A347756 Block[{a, u = {1}, v = 1}, a = Import["https://oeis.org/A347113/b347113.txt", "Data"][[All, -1]]; Do[If[a[[i]] == v, While[! FreeQ[a[[1 ;; i]], v], v++]]; AppendTo[u, v], {i, Length[a]}];  Union@ u]
%o A347756 (Python)
%o A347756 from math import gcd
%o A347756 A347756_list, nset, m, j = [1], {1}, 2, 2
%o A347756 for _ in range(10**4):
%o A347756     k = m
%o A347756     while k == j or gcd(k,j) == 1 or k in nset:
%o A347756         k += 1
%o A347756     j = k + 1
%o A347756     nset.add(k)
%o A347756     if k == m:
%o A347756         A347756_list.append(k)
%o A347756     while m in nset:
%o A347756         m += 1 # _Chai Wah Wu_, Sep 13 2021
%Y A347756 Cf. A008578, A347113, A347307, A347755, A347757.
%K A347756 nonn
%O A347756 1,2
%A A347756 _Michael De Vlieger_, Sep 12 2021