Voozh

A366610

Number of successive occurrences of the same first digits in A366585.

1, 1, 1, 1, 4, 5, 4, 2, 2, 2, 2, 1, 1, 97, 50, 34, 25, 20, 17, 14, 13, 11, 995, 500, 334, 250, 200, 167, 143, 125, 111, 9996, 5000, 3334, 2500, 2000, 1667, 1428, 1250, 1112, 99992, 50000, 33334, 25000, 20000, 16667, 14286, 12500, 11111, 999995, 500000, 333334, 250000, 200000, 166667, 142857

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..2000

EXAMPLE

a(6) = 5 because in A366585, the sixth run of same first digit of the terms lasts through five terms: 2021, 2223, 2425, 2627, 2829, each beginning with 2.

PROG

(PARI) lista(nn) = my(list=List(), k=1); while (k < nn, my(s="", n=digits(k)[1]); for (j=1, n, s = concat(s, Str(k+j-1)); ); listput(list, eval(s)); k += n; ); my(w = apply(x->digits(x)[1], list)); my(list=List(), last=w[1], nb=1); for (i=2, #w, if (w[i] == last, nb++, listput(list, nb); last=w[i]; nb=1; ); ); Vec(list, #list-1); \\ Michel Marcus, Oct 15 2023

(Python)

from itertools import islice

def A366610_gen(): # generator of terms

a, c = 1, 0

while (c:=c+1):

yield c

c, r = divmod((w:=((t:=int(str(a:=a+int(str(a)[0]))[0]))+1)*10**(len(str(a))-1)-1)-a, t)

a = w-r

A366610_list = list(islice(A366610_gen(), 30)) # Chai Wah Wu, Nov 04 2023

CROSSREFS

Cf. A366585.

Sequence in context: A092141 A120867 A011427 * A388173 A175622 A071413