A382067 Lexicographically earliest sequence of distinct positive integers such that the product of two consecutive terms is always a factorial number.
1, 2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, 2027025, 3072, 155925, 256, 14175, 2816, 170100, 36608, 2381400, 549120, 11340, 32, 1260, 4, 6, 20, 36, 140, 288, 12600, 3168, 151200, 24, 5, 144, 35, 1152, 315, 16, 45, 112, 360, 14, 2880
Offset: 1
Keywords
Examples
The first terms are: n a(n) a(n)*a(n+1) -- ------- ----------- 1 1 2! 2 2 3! 3 3 4! 4 8 5! 5 15 6! 6 48 7! 7 105 8! 8 384 9! 9 945 10! 10 3840 11! 11 10395 12! 12 46080 13! 13 135135 14! 14 645120 15! 15 2027025 13! 16 3072 12!
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
- Rémy Sigrist, PARI program
Programs
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PARI
\\ See Links section.
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Python
from itertools import count, islice def agen(): # generator of terms fset, aset, an = set(), set(), 1 while True: yield an aset.add(an) fk = 1 for k in count(2): fk *= k q, r = divmod(fk, an) if r == 0 and q not in aset: an = q break print(list(islice(agen(), 48))) # Michael S. Branicky, Mar 14 2025
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