A384644 a(n) is the least k such that {A007504(1), A007504(2), ..., A007504(k)} mod n = {0,...,n-1}.

1, 2, 10, 20, 10, 57, 18, 24, 20, 35, 25, 97, 49, 27, 67, 43, 115, 113, 60, 62, 97, 50, 107, 187, 98, 92, 72, 94, 66, 230, 125, 132, 191, 130, 180, 168, 91, 113, 142, 199, 157, 305, 184, 224, 242, 229, 119, 297, 200, 292, 179, 133, 198, 341, 357, 286, 324, 329

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..3000

Example

a(3) = 10: {2, 2, 1, 2, 1, 2, 1, 2, 1, 0} (2 mod 3 = 2, (2 + 3) mod 3 = 2, (2 + 3 + 5) mod 3 = 1, etc.).
a(4) = 20: {2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 3}.

Prog

(PARI) a(n)={my(m=Map, s=0); for(i=1, oo, s+=prime(i); mapput(m, s%n, 1); if(#Vec(m)==n, return(i)))}
(Python)
from sympy import nextprime
def a(n):
    k, p, residues, A007504_k = 0, 2, set(), 2
    while len(residues) < n:
        k, p, residues = k+1, nextprime(p), residues | {A007504_k%n}
        A007504_k += p
    return k
print([a(n) for n in range(1, 59)]) # Michael S. Branicky, Jun 12 2025

Crossrefs

Cf. A007504.

Sequence in context: A342539 A346810 A347024 * A009342 A357486 A350508

Adjacent sequences: A384641 A384642 A384643 * A384645 A384646 A384647

Keyword

nonn

Author

Charles L. Hohn, Jun 05 2025

Status

approved