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.

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, 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, 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

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..10080

Example

   a(0) =  0 (by definition)
   a(1) =  1 ('1' in factorial base), as 0 has occurred once in all the preceding terms.
   a(2) =  1 as 1 has occurred once in all the preceding terms.
   a(3) =  2 ('10' in factorial base), as digit '1' has occurred two times in total in all the preceding terms.
   a(4) =  3 ('11' in factorial base), as '1' occurs once in each a(1) and a(2) and a(3).
   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).
   a(6) =  1 ('1' in factorial base), as '2' so far occurs only once at a(5)
   a(7) =  7 = '101'
   a(8) =  9 = '111'
   a(9) = 12 = '200'
  a(10) =  2 = '2'
  a(11) = 13 = '201'
  a(12) =  3 = '11'
  a(12) =  3 = '11'
  a(13) = 16 = '220'
  a(14) =  5 = '21'
  a(15) =  6 = '100'
  a(16) = 18 = '300'
  a(17) =  1 = '1'
  a(18) = 19 = '301'
  a(19) =  2 = '10'
  a(20) = 21 = '311'
  a(21) =  3 = '11'
  a(22) = 25 = '1001'
  a(23) = 27 = '1011'
  a(24) = 30 = '1100'
  a(25) = 32 = '1110'
  a(26) = 35 = '1121'
  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).

Prog

(MIT/GNU Scheme with memoizing definec-macro from Antti Karttunen's IntSeq-library)
(definec (A249070 n) (if (zero? n) n (vector-ref (A249070aux_digit_counts (- n 1)) (A246359 (A249070 (- n 1))))))
(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)))))))))

Crossrefs

Cf. A007623, A246359, A249146, A249150.

Differs from A249069 for the first time at n=27, where a(27) = 7, while A249069(27) = 38.

Sequence in context: A330612 A121053 A203620 * A249069 A191308 A191399

Adjacent sequences: A249067 A249068 A249069 * A249071 A249072 A249073

Keyword

nonn,base

Author

Antti Karttunen, Oct 20 2014

Status

approved