A249069 a(n+1) gives the number of occurrences of the first digit of a(n) in factorial base (i.e., A099563(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, 38, 40, 41, 43, 45, 48, 13, 14, 15, 16, 18, 6, 53, 20, 7, 57, 21, 8, 64, 24, 65, 27, 69, 28, 72, 10, 73, 11, 76, 12, 33, 80, 13, 34, 85, 14, 37, 89, 15, 41, 94, 17, 46, 96, 1, 97, 2, 99, 3, 103, 4, 48, 49, 50

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 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) = 38 = '1210' as the leftmost digit '1' has occurred 38 times in total in the factorial base expansions of the preceding terms a(0) - a(26).
etc.

Prog

(MIT/GNU Scheme with memoizing definec-macro from Antti Karttunen's IntSeq-library)
(definec (A249069 n) (if (zero? n) n (vector-ref (A249069aux_digit_counts (- n 1)) (A099563 (A249069 (- n 1))))))
(definec (A249069aux_digit_counts n) (cond ((zero? n) (vector 1)) (else (let* ((start_n (A249069 n)) (copy-of-prevec (vector-copy (A249069aux_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. A249009 (analogous sequence in base-10).

Differs from a variant A249070 for the first time at n=27, where a(27) = 38, while A249070(27) = 7.

Cf. also A007623, A099563, A246359.

Sequence in context: A121053 A203620 A249070 * A191308 A191399 A191316

Adjacent sequences: A249066 A249067 A249068 * A249070 A249071 A249072

Keyword

nonn,base

Author

Antti Karttunen, Oct 20 2014

Status

approved