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A350329
a(n) is the least positive integer such that 2^n + a(n)*n*(n+1) equals a power of 2.
1
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
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
Sequence in context: A305753 A181813 A059187 * A265458 A054916 A194767
KEYWORD
nonn
AUTHOR
Ali Sada, Dec 26 2021
EXTENSIONS
More terms from Amiram Eldar, Dec 26 2021
STATUS
approved