A366477 a(n) = smallest k such that A366475(k) >= n, or -1 if no such k exists.

2, 3, 29, 28025, 2467754261

Offset: 1

Author

N. J. A. Sloane, Oct 26 2023

Keywords

• nonn
• more

Crossrefs

Cf. A364054, A366475.

Programs

Mathematica

nn = 2^16; c[] := False; m[] := 0; j = 1; c[0] = c[1] = True; q[_] := 0; s = -1;
  Monitor[Do[p = Prime[n - 1]; r = Mod[j, p];
    While[Set[k, p m[p] + r ]; c[k], m[p]++];
    (If[q[#] == 0, Set[q[#], n]]; If[# > s, s = #]) &[ m[p] ];
    Set[{c[k], j}, {True, k}], {n, 2, nn}], n];
Array[q, s] (* Michael De Vlieger, Oct 27 2023 *)

Python

from itertools import count
from sympy import nextprime
def A366477(n):
    a, aset, p = 1, {0,1}, 1
    for i in count(2):
        p = nextprime(p)
        b = a%p
        for j in count(0):
            if b not in aset:
                aset.add(b)
                a = b
                break
            b += p
        if j>=n:
            return i # Chai Wah Wu, Oct 27 2023

Extensions

a(4) = 28025 from Michael De Vlieger, Oct 26 2023, who also reports that 5 does not appear in the first 2^24 terms of A366475.

a(5) from Chai Wah Wu, Oct 28 2023