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 A275947 Number of distinct slopes with multiple nonzero digits in factorial base representation of n: a(n) = A056170(A275734(n)). (See comments for more exact definition) 9
 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,60 COMMENTS a(n) gives the number of distinct elements that have multiplicity > 1 in a multiset [(i_x - d_x) | where d_x ranges over each nonzero digit present and i_x is its position from the right]. LINKS Antti Karttunen, Table of n, a(n) for n = 0..40320 Indranil Ghosh, Python program for computing this sequence FORMULA a(n) = A056170(A275734(n)). Other identities and observations. For all n >= 0. a(n) = A275949(A225901(n)). A060502(n) = A275946(n) + a(n). a(n) <= A275962(n). EXAMPLE For n=525, in factorial base "41311", there are three occupied slopes. The maximal slope contains the nonzero digits "3.1", the sub-maximal digits "4..1.", and the sub-sub-sub-maximal just "1..." (the 1 in the position 4 from right is the sole occupier of its own slope). Thus there are two slopes with more than one nonzero digit, and a(525) = 2. Equally, when we form a multiset of (digit-position - digit-value) differences for all nonzero digits present in "41311", we obtain a multiset [0, 0, 1, 1, 3], in which the distinct elements that occur multiple times are 0 and 1, thus a(525) = 2. PROG (Scheme) (define (A275947 n) (A056170 (A275734 n))) CROSSREFS Cf. A056170, A275734. Cf. A275804 (indices of zeros), A275805 (of nonzeros). Cf. also A060502, A225901, A275946, A275949, A275962. Sequence in context: A285716 A101606 A257469 * A337976 A125005 A309367 Adjacent sequences:  A275944 A275945 A275946 * A275948 A275949 A275950 KEYWORD nonn,base AUTHOR Antti Karttunen, Aug 15 2016 STATUS approved

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Last modified June 18 17:32 EDT 2021. Contains 345120 sequences. (Running on oeis4.)