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A347757 Indices of local minima in A347113.

%I A347757 #18 Sep 19 2021 14:47:03
%S A347757 1,8,11,20,28,37,51,53,101,116,136,146,159,213,302,318,440,520,638,
%T A347757 698,702,912,1031,1128,1528,1758,1832,1891,2107,2198,2523,2671,2857,
%U A347757 3069,3760,3892,3946,4256,4438,4638,4880,5022,5656,6092,6147,6322,6470,6492,6579
%N A347757 Indices of local minima in A347113.
%C A347757 a(n)-1 = last instance of A347756(n) in A347755.
%C A347757 a(n+1) > a(n) + 1, since terms in A347113 are distinct by definition.
%H A347757 Chai Wah Wu, <a href="/A347757/b347757.txt">Table of n, a(n) for n = 1..6904</a> (terms 1..898 from Michael De Vlieger)
%t A347757 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]; Map[FirstPosition[a, #][[1]] &, Most@ Union@ v]]
%t A347757 (* or using A347113 bfile: *)
%t A347757 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]}]; Map[FirstPosition[a, #][[1]] &, Most@ Union@ u] ]
%o A347757 (Python)
%o A347757 from math import gcd
%o A347757 A347757_list, nset, m, j, i = [1], {1}, 2, 2, 1
%o A347757 for _ in range(10**4):
%o A347757     i += 1
%o A347757     k = m
%o A347757     while k == j or gcd(k,j) == 1 or k in nset:
%o A347757         k += 1
%o A347757     j = k + 1
%o A347757     nset.add(k)
%o A347757     if k == m:
%o A347757         A347757_list.append(i)
%o A347757     while m in nset:
%o A347757         m += 1 # _Chai Wah Wu_, Sep 13 2021
%Y A347757 Cf. A347113, A347306 (indices of records in A347113), A347755, A347756.
%K A347757 nonn
%O A347757 1,2
%A A347757 _Michael De Vlieger_, Sep 12 2021