A275956 - OEIS

%I #14 Aug 17 2016 22:17:54

%S 0,1,2,4,6,10,11,12,13,15,17,18,20,21,24,28,29,36,38,42,43,48,49,50,

%T 53,55,56,58,59,62,66,68,69,70,72,73,75,76,78,80,82,83,88,91,92,93,94,

%U 96,98,99,102,103,108,112,120,124,125,132,134,138,139,166,167,168,174,186,187,190,191,192,194,196,197,205,207,208,209,214,215,216,217,226

%N Numbers n for which A060502(n) = A275806(n); numbers whose factorial base representation has an equal number of distinct nonzero digits and occupied slopes.

%C Nonnegative integer n is included here iff the number of distinct nonzero digits elements present in its factorial base representation is equal to the number of distinct elements in a multiset [(i_x - d_x) | where d_x ranges over each (not all necessarily distinct) nonzero digit present and i_x is that digit's position from the right].

%C If n is included, then A153880(n), A255411(n) and A225901(n) are also included.

%H Antti Karttunen, <a href="/A275956/b275956.txt">Table of n, a(n) for n = 0..12558</a>

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

%e 11 ("121" in factorial base) is included, as there are two occupied slopes (3-1 = 2 and 2-2 = 1-1 = 0) and also two distinct nonzero digits, namely 1 and 2.

%e 59 ("2121" in factorial base) is included, as there are two occupied slopes (4-2 = 3-1 and 2-2 = 1-1) and also two distinct nonzero digits, namely 1 and 2.

%e 226 ("14120") is included, as there are three occupied slopes (5-1 = 4, 4-4 = 2-2 = 0, 3-1 = 2) and also three distinct nonzero digits, 1, 2 and 4.

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A275956 (ZERO-POS 0 0 (lambda (n) (- (A060502 n) (A275806 n)))))

%Y Cf. A060502, A275806.

%Y Cf. A153880, A255411, A225901.

%Y Cf. A000142, A275959 (subsequences).

%K nonn,base

%O 0,3

%A _Antti Karttunen_, Aug 16 2016