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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.
0
1, 2, 14, 135, 1349, 13490, 134903, 1349038, 13490389, 134903902, 1349039036, 13490390385, 134903903876, 1349039038789, 13490390387923, 134903903879272, 1349039038792762, 13490390387927663, 134903903879276676, 1349039038792766810, 13490390387927668159
OFFSET
1,2
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
EXAMPLE
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.
PROG
(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
CROSSREFS
Sequence in context: A326886 A111424 A317356 * A336182 A224729 A355722
KEYWORD
nonn,base
AUTHOR
Rodolfo Kurchan, Aug 18 2024
EXTENSIONS
a(17)-a(21) from Pontus von Brömssen, Aug 18 2024
STATUS
approved