A249009 a(n+1) gives the number of occurrences of the first digit of a(n) so far, up to and including a(n), with a(0)=0.

0, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 2, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 3, 10, 21, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 4, 10, 23, 5, 5, 6, 5, 7, 5, 8, 5, 9, 5, 10, 24, 6, 6, 7, 6, 8, 6, 9, 6, 10

Offset

0,4

Comments

Inspired by A248034.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Alois P. Heinz, Graph of 10^6 terms

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      coeff(b(n-1), x, convert(a(n-1), base, 10)[-1] ))
    end:
b:= proc(n) option remember; `if`(n=0, 1, b(n-1)+
      add(x^i, i=convert(a(n), base, 10)))
    end:
seq(a(n), n=0..120);

Prog

(MIT/GNU Scheme with memoizing definec-macro from Antti Karttunen's IntSeq-library)
(definec (A249009 n) (if (zero? n) n (vector-ref (A249009aux_digit_counts (- n 1)) (A000030 (A249009 (- n 1))))))
(definec (A249009aux_digit_counts n) (cond ((zero? n) (vector 1 0 0 0 0 0 0 0 0 0)) (else (let loop ((digcounts-for-n (vector-copy (A249009aux_digit_counts (- n 1)))) (n (A249009 n))) (cond ((zero? n) digcounts-for-n) (else (vector-set! digcounts-for-n (modulo n 10) (+ 1 (vector-ref digcounts-for-n (modulo n 10)))) (loop digcounts-for-n (floor->exact (/ n 10)))))))))
(define (A000030 n) (let loop ((n n)) (if (< n 10) n (loop (floor->exact (/ n 10))))))
;; Antti Karttunen, Oct 20 2014
(Python)
from itertools import islice
def A249009_gen(): # generator of terms
    c, clist = 0, [1]+[0]*9
    while True:
        yield c
        c = clist[int(str(c)[0])]
        for d in str(c):
            clist[int(d)] += 1
A249009_list = list(islice(A249009_gen(), 100)) # Chai Wah Wu, Dec 13 2022

Crossrefs

Cf. A248034, A000030.

Cf. A249069 (analogous sequence in factorial base).

Sequence in context: A356348 A336514 A358851 * A162520 A342703 A249068

Adjacent sequences: A249006 A249007 A249008 * A249010 A249011 A249012

Keyword

nonn,look,base

Author

Alois P. Heinz, Oct 18 2014

Status

approved