A366475 a(n) = (A364054(n) - A366470(n))/prime(n-1).

1, 2, 2, 0, 1, 0, 1, 2, 2, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 3, 0, 2, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 1, 2, 2, 1, 2, 1, 2, 0, 1, 2, 0, 2, 0

Offset: 2

Author

N. J. A. Sloane, Oct 26 2023

Keywords

• nonn

Comments

a(29) = 3. When, if ever, does 4 appear?

Answer: a(28025) = 4. - Michael De Vlieger, Oct 26 2023

Examples

			   n p(n-1)  x   y  a(n)  [x = A364054(n), y = A366470(n)]
   1   (1)   1   -   -    [a(n) = (x-y)/p(n-1)]
   2    2    3   1   1
   3    3    6   0   2
   4    5   11   1   2
   5    7    4   4   0
   6   11   15   4   1
   7   13    2   2   0
...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 2..65536
• Michael De Vlieger, 2048 X 2048 raster showing a(n), n = 1..4194304 in rows of 2048 terms, left to right, then continued below for 2048 rows total. Color indicates terms as follows: black = 0, blue = 1, green = 2, gold = 3, red = 4.

Crossrefs

Cf. A364054, A366470, A366477 (records).

Programs

Mathematica

nn = 2^20;
  c[] := False; m[] := 0; a[1] = 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], b[n], c[k], j}, {k, m[p], True, k}], {n, 2, nn}], n];
Array[b, nn-1, 2] (* Michael De Vlieger, Oct 26 2023 *)

Python

from itertools import count, islice
from sympy import nextprime
def A366475_gen(): # generator of terms
    a, aset, p = 1, {0,1}, 1
    while True:
        p = nextprime(p)
        b = a%p
        for i in count(0):
            if b not in aset:
                aset.add(b)
                a = b
                break
            b += p
        yield i
A366475_list = list(islice(A366475_gen(),30)) # Chai Wah Wu, Oct 27 2023