A366911 a(n) = (A364054(n+1) - A364054(n)) / prime(n) (where prime(n) denotes the n-th prime number).

1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -3, 2, -2, 1, -1, 1, -1, 2, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1

Offset: 1

Author

Rémy Sigrist, Oct 27 2023

Keywords

• sign

Comments

a(n) is the number of steps of size prime(n) in going from A364054(n) to A364054(n+1).

Examples

			a(7) = (A364054(8) - A364054(7)) / prime(7) = (19 - 2) / 17 = 1.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..9999
• Rémy Sigrist, PARI program

Crossrefs

Cf. A160357, A364054, A366912 (partial sums).

Programs

Mathematica

nn = 2^16; 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}, {(k - j)/p, True, k}], {n, 2, nn + 1}], n];
Array[a, nn] (* Michael De Vlieger, Oct 27 2023 *)

PARI

See Links section.

Python

from itertools import count, islice
from sympy import nextprime
def A366911_gen(): # generator of terms
    a, aset, p = 1, {0,1}, 2
    while True:
        k, b = divmod(a,p)
        for i in count(-k):
            if b not in aset:
                aset.add(b)
                a, p = b, nextprime(p)
                yield i
                break
            b += p
A366911_list = list(islice(A366911_gen(),30)) # Chai Wah Wu, Oct 27 2023