A350329 a(n) is the least positive integer such that 2^n + a(n)*n*(n+1) equals a power of 2.

1, 2, 2, 12, 16, 96, 16, 224, 23296, 9761280, 15872, 107520, 184320, 319488, 2048, 61440, 7186350080, 200933376, 94812623732736, 10223616, 4874025566208, 10759916740583034417814216835787128832, 63739789312, 29320282112, 59516348042566359318528

Offset

1,2

Comments

We can always find a value for a(n). It is an elementary consequence of Fermat's little theorem, Hensel's lemma, and the Chinese remainder theorem, that more generally for every pair of positive integers u,v there exist x,y such that x*u = (2^y - 1)*2^v. - Fred Lunnon, Dec 26 2021 in SeqFan

Links

Table of n, a(n) for n=1..25.

Example

2^5 + 16*30 = 512, so a(5) = 16.

Mathematica

a[n_] := Module[{ob = n*(n + 1), pow = 2^n, k = n + 1}, While[! Divisible[2^k - pow, ob], k++]; (2^k - pow)/ob]; Array[a, 25] (* Amiram Eldar, Dec 26 2021 *)

Prog

(Python)
def A350329(n):
    a, b, c = 2**n, n*(n+1), 2**(n+1)
    while (x := divmod(c-a, b))[1] != 0:
        c *= 2
    return x[0] # Chai Wah Wu, Jan 07 2022

Crossrefs

Cf. A000079, A002378.

Sequence in context: A305753 A181813 A059187 * A265458 A054916 A194767

Adjacent sequences: A350326 A350327 A350328 * A350330 A350331 A350332

Keyword

nonn

Author

Ali Sada, Dec 26 2021

Extensions

More terms from Amiram Eldar, Dec 26 2021

Status

approved