A086493 Group the natural numbers such that the n-th group sum is divisible by prime(n): (1, 2, 3), (4, 5), (6, 7, 8, 9), (10, 11), (12, 13, 14, 15, 16, 17, 18, 19, 20, 21), ... Sequence contains the first term of every group.

1, 4, 6, 10, 12, 22, 31, 38, 39, 54, 63, 93, 130, 158, 187, 190, 235, 238, 251, 286, 354, 377, 414, 417, 474, 497, 514, 517, 554, 646, 711, 814, 890, 892, 916, 1022, 1093, 1106, 1177, 1329, 1440, 1604, 1655, 1784, 1884, 2057, 2123, 2309, 2375, 2393, 2417, 2477

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)

Mathematica

k = 0; Table[p = Prime[n]; k++; first = k; sm = 0; While[sm = sm + k; Mod[sm, p] > 0, k++]; first, {n, 50}] (* T. D. Noe, Mar 19 2014 *)

Prog

(Python)
from itertools import count
from sympy import prime, primerange
def aupton(terms):
    alst, naturals = [], count(1)
    for p in primerange(1, prime(terms)+1):
        s = start = next(naturals)
        while s%p: s += next(naturals)
        alst.append(start)
    return alst
print(aupton(52)) # Michael S. Branicky, Jun 09 2021

Crossrefs

Cf. A086491, A086492.

Sequence in context: A310581 A310582 A177929 * A234965 A320881 A224796

Adjacent sequences: A086490 A086491 A086492 * A086494 A086495 A086496

Keyword

nonn

Author

Amarnath Murthy, Jul 28 2003

Extensions

More terms from Ray Chandler and Gabriel Cunningham (gcasey(AT)mit.edu), Sep 16 2003

Status

approved