A366470 a(n) = A364054(n-1) mod prime(n-1).

1, 0, 1, 4, 4, 2, 2, 0, 15, 3, 1, 26, 26, 24, 24, 18, 18, 16, 16, 12, 12, 6, 81, 81, 73, 73, 71, 63, 57, 57, 29, 29, 23, 23, 13, 13, 1, 158, 154, 154, 148, 148, 138, 138, 134, 134, 122, 122, 118, 118, 114, 114, 112, 112, 106, 106, 100, 100, 94, 94, 92

Offset: 2

Author

N. J. A. Sloane, Oct 21 2023

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..10000
• Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.
• Michael De Vlieger, Log log scatterplot of a(n), n = 2..2^20, showing a(n) = 0 instead as a(n) = 1/10, with a color function showing b(n) = 0 in black, b(n) = 1 in blue, b(n) = 2 in green, b(n) = 3 in chartreuse, and b(n) = 4 in red, where b() = A366475(). (The plot accentuates larger values of b(n) through larger size, so adjacent smaller values may be eclipsed.)
• Chai Wah Wu, Graph of first 10^8 terms

Crossrefs

Cf. A364054, A366475.

Programs

Mathematica

nn = 2^20; c[] := False; m[] := 0; j = 1; c[0] = c[1] = True;
  Monitor[Do[p = Prime[n - 1]; r = Mod[j, p];
    While[Set[k, p m[p] + r ]; c[k], m[p]++];
    Set[{a[n - 1], c[k], j}, {r, True, k}], {n, 2, nn + 1}], n];
Array[a, nn] (* Michael De Vlieger, Oct 27 2023 *)

Python

from itertools import count, islice
from sympy import nextprime
def A366470_gen(): # generator of terms
    a, aset, p = 1, {0,1}, 2
    while True:
        yield a
        for b in count(a,p):
            if b not in aset:
                aset.add(b)
                a = b%(p:=nextprime(p))
                break
A366470_list = list(islice(A366470_gen(),30)) # Chai Wah Wu, Oct 22 2023

Formula

A364054(n) = A366475(n)*prime(n-1) + a(n) for n > 1. - Michael De Vlieger, Mar 06 2024