A347757 Indices of local minima in A347113.

1, 8, 11, 20, 28, 37, 51, 53, 101, 116, 136, 146, 159, 213, 302, 318, 440, 520, 638, 698, 702, 912, 1031, 1128, 1528, 1758, 1832, 1891, 2107, 2198, 2523, 2671, 2857, 3069, 3760, 3892, 3946, 4256, 4438, 4638, 4880, 5022, 5656, 6092, 6147, 6322, 6470, 6492, 6579

Offset: 1

Author

Michael De Vlieger, Sep 12 2021

Keywords

• nonn

Comments

a(n)-1 = last instance of A347756(n) in A347755.

a(n+1) > a(n) + 1, since terms in A347113 are distinct by definition.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..6904 (terms 1..898 from Michael De Vlieger)

Crossrefs

Cf. A347113, A347306 (indices of records in A347113), A347755, A347756.

Programs

Mathematica

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]]
(* or using A347113 bfile: *)
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] ]

Python

from math import gcd
A347757_list, nset, m, j, i = [1], {1}, 2, 2, 1
for _ in range(10**4):
    i += 1
    k = m
    while k == j or gcd(k,j) == 1 or k in nset:
        k += 1
    j = k + 1
    nset.add(k)
    if k == m:
        A347757_list.append(i)
    while m in nset:
        m += 1 # Chai Wah Wu, Sep 13 2021