A352928 The smallest unused number when A093714(n) is being calculated.

1, 2, 2, 4, 4, 6, 6, 8, 8, 9, 9, 10, 10, 10, 12, 12, 15, 15, 16, 16, 16, 18, 18, 20, 20, 24, 24, 24, 24, 28, 28, 28, 28, 30, 30, 30, 30, 34, 34, 36, 36, 36, 36, 40, 40, 42, 42, 42, 42, 42, 42, 48, 48, 50, 50, 54, 54, 54, 54, 58, 58, 60, 60, 60, 60, 64, 64, 66, 66, 66, 66, 70, 70

Offset: 1

Author

N. J. A. Sloane, May 02 2022

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A093714.

Programs

Mathematica

nn = 120; c[] = 0; a[1] = c[1] = 1; u = 2; {1}~Join~Reap[Do[k = u; While[Nand[c[k] == 0, CoprimeQ[#, k], k != # + 1], k++] &@ a[i - 1]; Set[{a[i], c[k]}, {k, i}]; If[a[i] == u, While[c[u] > 0, u++]], {i, 2, nn}]][[-1, -1]] (* _Michael De Vlieger, May 02 2022 *)

Python

from math import gcd
from itertools import islice
def agen(): # generator of terms
    an, aset, mink = 1, {1}, 2
    yield 1
    while True:
        yield mink
        k = mink
        while k in aset or gcd(an, k) != 1 or k-an == 1: k += 1
        an = k
        aset.add(an)
        while mink in aset: mink += 1
print(list(islice(agen(), 72))) # Michael S. Branicky, May 02 2022