A347756 Local minima in A347113.

1, 2, 3, 7, 11, 17, 19, 23, 31, 37, 59, 61, 67, 79, 97, 151, 157, 199, 211, 229, 271, 307, 337, 367, 499, 577, 601, 619, 691, 727, 829, 877, 937, 1009, 1237, 1279, 1297, 1399, 1459, 1531, 1609, 1657, 1867, 2011, 2029, 2089, 2131, 2137, 2179, 2281, 2311, 2467, 2539

Offset

1,2

Comments

Distinct terms in A347755.

Conjecture: subset of A008578.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..6626 (terms n = 1..899 from Michael De Vlieger)

Michael De Vlieger, Log-log scatterplot of A347113(n) for 1 <= n <= 2^12, showing terms in A347307 in red, those in A347755 joined in gold, and terms in this sequence in blue.

Formula

A347757(n) = index of a(n) in A347113.

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]; 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]}];  Union@ u]

Prog

(Python)
from math import gcd
A347756_list, nset, m, j = [1], {1}, 2, 2
for _ in range(10**4):
    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:
        A347756_list.append(k)
    while m in nset:
        m += 1 # Chai Wah Wu, Sep 13 2021

Crossrefs

Cf. A008578, A347113, A347307, A347755, A347757.

Sequence in context: A368403 A361857 A197636 * A040103 A045323 A161185

Adjacent sequences: A347753 A347754 A347755 * A347757 A347758 A347759

Keyword

nonn

Author

Michael De Vlieger, Sep 12 2021

Status

approved