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

1,2

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)

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] ]

Prog

(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

Crossrefs

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

Sequence in context: A213084 A243520 A129730 * A368356 A291664 A318347

Adjacent sequences: A347754 A347755 A347756 * A347758 A347759 A347760

Keyword

nonn

Author

Michael De Vlieger, Sep 12 2021

Status

approved