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A369407
A variant of A008336 based on polynomials over GF(2) (see Comments for precise definition).
1
1, 2, 6, 24, 120, 20, 108, 864, 96, 960, 6720, 624, 6192, 37152, 491232, 30702, 1806, 127, 1905, 27348, 486596, 25102, 1890, 19760, 456624, 5581280, 439712, 21624, 451032, 5199760, 123954032, 3966529024, 123317760, 3850804224, 127210628096, 4070965504
OFFSET
1,2
COMMENTS
Let P(m) denote the polynomial over GF(2) whose coefficients are encoded in the binary expansion of the nonnegative integer m.
Let b(1) = 1 and for any n > 0, if P(n) divides b(n) then b(n+1) = b(n) / P(n), otherwise b(n+1) = b(n) * P(n).
For any n > 0, a(n) is the unique number v such that P(v) = b(n).
EXAMPLE
The first terms, alongside the corresponding polynomials, are:
n a(n) b(n) P(n)
-- ---- --------------------- -----------
1 1 1 1
2 2 X X
3 6 X^2 + X X + 1
4 24 X^4 + X^3 X^2
5 120 X^6 + X^5 + X^4 + X^3 X^2 + 1
6 20 X^4 + X^2 X^2 + X
7 108 X^6 + X^5 + X^3 + X^2 X^2 + X + 1
8 864 X^9 + X^8 + X^6 + X^5 X^3
9 96 X^6 + X^5 X^3 + 1
10 960 X^9 + X^8 + X^7 + X^6 X^3 + X
PROG
(PARI) P(n) = Mod(1, 2) * Pol(binary(n))
P_1(p) = fromdigits(lift(Vec(p)), 2)
{ b = 1; for (n = 1, 36, p = P(n); if (b % p==0, b \= p, b *= p); print1 (P_1(b)", "); ); }
CROSSREFS
Cf. A008336.
Sequence in context: A362332 A092495 A110808 * A284567 A360300 A065422
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 22 2024
STATUS
approved