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A318358 a(1) = 2; for n > 1, a(n) is the least positive number not yet in the sequence such that Sum_{k=1..n} a(k) divides Sum_{k=1..n} a(k)^2. 2
2, 6, 5, 13, 9, 20, 30, 19, 52, 78, 18, 7, 43, 151, 79, 126, 88, 373, 183, 84, 177, 521, 263, 2347, 1305, 392, 294, 1207, 3946, 1973, 2099, 185, 999, 518, 1970, 9791, 4577, 6111, 4811, 21372, 10154, 3210, 9874, 89482, 49678, 9918, 8344, 46684, 65588, 50136 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Is this sequence infinite?

The variant of this sequence starting with 1 has only one term.

See A318359 for a similar sequence.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..250 (n = 1..100 from Rémy Sigrist)

EXAMPLE

For n = 3:

- (2^2 + 6^2 + 1^2) == 5 mod (2 + 6 + 1),

- (2^2 + 6^2 + 3^2) == 5 mod (2 + 6 + 3),

- (2^2 + 6^2 + 4^2) == 8 mod (2 + 6 + 4),

- (2^2 + 6^2 + 5^2) == 0 mod (2 + 6 + 5),

- hence a(3) = 5.

PROG

(PARI) s=0; s2=0; p=0; v=2; for (n=1, 50, print1 (v ", "); s+=v; s2+=v^2; p+=2^v; for (w=1, oo, if (!bittest(p, w) && (s2+w^2)%(s+w)==0, v=w; break)))

(Python)

import bisect

from sympy.solvers.diophantine import diop_quadratic

from sympy.abc import x, y

A318358_list, A318358_set, p, q = [2], {2}, 2, 2**2

for _ in range(100):

    r = sorted(next(zip(*diop_quadratic(x**2+q-p*y-x*y))))

    for a in r[bisect.bisect_right(r, 0):]:

        if a not in A318358_set:

            A318358_list.append(a)

            A318358_set.add(a)

            break

    p += a

    q += a**2 # Chai Wah Wu, Aug 28 2018

CROSSREFS

Cf. A318359.

Sequence in context: A179627 A193977 A092313 * A230383 A009460 A085205

Adjacent sequences:  A318355 A318356 A318357 * A318359 A318360 A318361

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Aug 24 2018

STATUS

approved

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Last modified April 23 22:17 EDT 2019. Contains 322388 sequences. (Running on oeis4.)