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A248034 a(n+1) gives the number of occurrences of the last digit of a(n) so far, up to and including a(n), with a(0)=0. 10
0, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 10, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 3, 10, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 4, 10, 5, 5, 6, 5, 7, 5, 8, 5, 9, 5, 10, 6, 6, 7, 6, 8, 6, 9, 6, 10, 7, 7, 8, 7, 9, 7, 10, 8, 8, 9, 8, 10, 9, 9, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

In other words, the number to the right of a comma gives the number of occurrences of the digit immediately to the left of the comma, counting from the beginning up to that digit or comma.

LINKS

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

E. Angelini, Digit-counters updating themselves, SeqFan list, Oct 11 2014

Zak Seidov, Graph of 10^6 terms

MAPLE

a:= proc(n) option remember; `if`(n=0, 0,

      coeff(b(n-1), x, irem(a(n-1), 10)))

    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);  # Alois P. Heinz, Oct 18 2014

PROG

(PARI) c=vector(10); print1(a=0); for(n=1, 99, apply(d->c[d+1]++, if(a, digits(a))); print1(", "a=c[1+a%10]))

(MIT/GNU Scheme)

;; An implementation of memoization-macro definec can be found for example from: http://oeis.org/wiki/Memoization

(definec (A248034 n) (if (zero? n) n (vector-ref (A248034aux_digit_counts (- n 1)) (modulo (A248034 (- n 1)) 10))))

(definec (A248034aux_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 (A248034aux_digit_counts (- n 1)))) (n (A248034 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)))))))))

;; Antti Karttunen, Oct 22 2014

CROSSREFS

Cf. A249068 (analogous sequence in base 8).

Cf. A249009 (analogous sequence which uses the first, not the last digit).

Cf. also A249069, A249070, A249144, A249148.

Sequence in context: A318225 A335497 A309872 * A322182 A336514 A249009

Adjacent sequences:  A248031 A248032 A248033 * A248035 A248036 A248037

KEYWORD

nonn,base,look,hear

AUTHOR

Eric Angelini and M. F. Hasler, Oct 11 2014

STATUS

approved

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Last modified May 14 13:50 EDT 2021. Contains 343884 sequences. (Running on oeis4.)