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A249070 a(n+1) gives the number of occurrences of the maximum digit of a(n) in factorial base (i.e., A246359(a(n))) so far amongst the factorial base representations of all the terms up to and including a(n), with a(0)=0.

%I A249070 #13 Oct 25 2014 14:47:07
%S A249070 0,1,1,2,3,5,1,7,9,12,2,13,3,16,5,6,18,1,19,2,21,3,25,27,30,32,35,7,
%T A249070 40,9,44,4,10,11,12,13,14,15,16,18,5,19,6,56,20,7,61,22,8,64,26,66,9,
%U A249070 69,10,29,30,76,11,32,81,12,33,88,13,36,37,38,39,40,42,14,43,15,44,16,46,17,49,50,51,52
%N A249070 a(n+1) gives the number of occurrences of the maximum digit of a(n) in factorial base (i.e., A246359(a(n))) so far amongst the factorial base representations of all the terms up to and including a(n), with a(0)=0.
%H A249070 Antti Karttunen, <a href="/A249070/b249070.txt">Table of n, a(n) for n = 0..10080</a>
%e A249070    a(0) =  0 (by definition)
%e A249070    a(1) =  1 ('1' in factorial base), as 0 has occurred once in all the preceding terms.
%e A249070    a(2) =  1 as 1 has occurred once in all the preceding terms.
%e A249070    a(3) =  2 ('10' in factorial base), as digit '1' has occurred two times in total in all the preceding terms.
%e A249070    a(4) =  3 ('11' in factorial base), as '1' occurs once in each a(1) and a(2) and a(3).
%e A249070    a(5) =  5 ('21' in factorial base), as '1' occurs once in each of a(1), a(2) and a(3) and twice at a(4).
%e A249070    a(6) =  1 ('1' in factorial base), as '2' so far occurs only once at a(5)
%e A249070    a(7) =  7 = '101'
%e A249070    a(8) =  9 = '111'
%e A249070    a(9) = 12 = '200'
%e A249070   a(10) =  2 = '2'
%e A249070   a(11) = 13 = '201'
%e A249070   a(12) =  3 = '11'
%e A249070   a(12) =  3 = '11'
%e A249070   a(13) = 16 = '220'
%e A249070   a(14) =  5 = '21'
%e A249070   a(15) =  6 = '100'
%e A249070   a(16) = 18 = '300'
%e A249070   a(17) =  1 = '1'
%e A249070   a(18) = 19 = '301'
%e A249070   a(19) =  2 = '10'
%e A249070   a(20) = 21 = '311'
%e A249070   a(21) =  3 = '11'
%e A249070   a(22) = 25 = '1001'
%e A249070   a(23) = 27 = '1011'
%e A249070   a(24) = 30 = '1100'
%e A249070   a(25) = 32 = '1110'
%e A249070   a(26) = 35 = '1121'
%e A249070   a(27) =  7 (= '101' in factorial base), as the maximum digit in the factorial base representation of a(26), namely '2', has occurred in total 7 times in terms a(0) - a(26): once in each of a(5), a(9), a(11), a(14) and a(26), and twice in a(13).
%o A249070 (MIT/GNU Scheme with memoizing definec-macro from _Antti Karttunen_'s IntSeq-library)
%o A249070 (definec (A249070 n) (if (zero? n) n (vector-ref (A249070aux_digit_counts (- n 1)) (A246359 (A249070 (- n 1))))))
%o A249070 (definec (A249070aux_digit_counts n) (cond ((zero? n) (vector 1)) (else (let* ((start_n (A249070 n)) (copy-of-prevec (vector-copy (A249070aux_digit_counts (- n 1)))) (newsize (max (vector-length copy-of-prevec) (+ 1 (A246359 start_n)))) (digcounts-for-n (vector-grow copy-of-prevec newsize))) (let loop ((n start_n) (i 2)) (cond ((zero? n) digcounts-for-n) (else (vector-set! digcounts-for-n (modulo n i) (+ 1 (or (vector-ref digcounts-for-n (modulo n i)) 0))) (loop (floor->exact (/ n i)) (+ i 1)))))))))
%Y A249070 Cf. A007623, A246359, A249146, A249150.
%Y A249070 Differs from A249069 for the first time at n=27, where a(27) = 7, while A249069(27) = 38.
%K A249070 nonn,base
%O A249070 0,4
%A A249070 _Antti Karttunen_, Oct 20 2014