A375507 a(1) = 1. For n > 1; a(n) is equal to a(n-1) plus the decimal value of the concatenation of the first n-1 digits of the sequence.

1, 2, 14, 135, 1349, 13490, 134903, 1349038, 13490389, 134903902, 1349039036, 13490390385, 134903903876, 1349039038789, 13490390387923, 134903903879272, 1349039038792762, 13490390387927663, 134903903879276676, 1349039038792766810, 13490390387927668159

Offset: 1

Author

Rodolfo Kurchan, Aug 18 2024

Keywords

• nonn
• base

Examples

			For n = 4 we have that a(n-1) = a(3) = 14 and the decimal value of the concatenation of the first three digits of the sequence is 121, so a(4) = 14 + 121 = 135.
		

Programs

Python

from itertools import count
def A375507_list(nmax):
    a = [1]
    def digits():
        for i in count():
            for d in str(a[i]):
                yield int(d)
    diff = 0
    for n,d in enumerate(digits(),1):
        if n==nmax: return a
        diff = 10*diff+d
        a.append(a[-1]+diff) # Pontus von Brömssen, Aug 18 2024

Formula

a(n) ~ (c/9)*10^(n-1), where c = Sum_{n>=1} a(n)/10^(n*(n-1)/2) = 1.2141351349... . - Pontus von Brömssen, Aug 18 2024

Extensions

a(17)-a(21) from Pontus von Brömssen, Aug 18 2024