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

Offset: 1

Author

Tamas Sandor Nagy, Oct 14 2023

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

Cf. A366585.

Programs

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

Extensions

More terms from Michel Marcus, Oct 15 2023