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 A230412 a(n) = the number of ways to express n as a sum d1*(k1!-1) + d2*(k2!-1) + ... + dj*(kj!-1), where all k's are distinct and greater than one and each di is in range [1,ki]; the characteristic function of A219650. 11
 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 LINKS Antti Karttunen, Table of n, a(n) for n = 0..10079 FORMULA a(0)=1 and for n>=1, a(n) = [(A219650(A230413(n-1)) + A230405(A230413(n-1))) = n], where [] stands for Iverson bracket. EXAMPLE a(0)=1 as the only solution is an empty sum. 1 can be represented as 1*(2!-1), and this is the only solution, thus a(1) = 1. 2 can be represented (also uniquely) as 2*(2!-1) thus a(2) = 1. 3 and 4 cannot be represented as such a sum, thus a(3) = a(4) = 0. 5 can be represented (uniquely) as 1*(3!-1) thus a(5) = 1. 6 can be represented (uniquely) as 1*(3!-1) + 1*(2!-1), thus a(6) = 1. 7 can be represented (uniquely) as 1*(3!-1) + 2*(2!-1), thus a(7) = 1. 17 can be represented (uniquely) as 3*(3!-1) + 2*(2!-1), thus a(17) = 1. PROG (Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library) (definec (A230412 n) (if (zero? n) 1 (let ((k (A230413 (- n 1)))) (if (= (+ (A219650 k) (A230405 k)) n) 1 0)))) CROSSREFS The characteristic function of A219650. A219658 gives the positions of zeros. Together with A230413 (the partial sums) can be used to compute A230414, A230423 and A230424. This sequence relates to the factorial base representation (A007623) in a similar way as A079559 relates to the binary system. Sequence in context: A014024 A014039 A016410 * A115361 A115358 A325898 Adjacent sequences:  A230409 A230410 A230411 * A230413 A230414 A230415 KEYWORD nonn AUTHOR Antti Karttunen, Nov 02 2013 STATUS approved

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Last modified July 25 01:31 EDT 2021. Contains 346273 sequences. (Running on oeis4.)