OFFSET
1,2
COMMENTS
All k-digit numbers that divide 10^{k+1} + 1. - Franklin T. Adams-Watters, Apr 23 2008
Notice the infinite pattern m = (90..90..90)91 with 1m1/m = 21, e.g., 1911/91 = 190911/9091 = 19090911/909091 = 21 (see A095372). - Zak Seidov, Apr 22 2008
Corresponding numbers k such that k * a(n) = 1.a(n).1 where '.' stands for concatenation are in A351320. - Bernard Schott, Feb 07 2022
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..1441 (terms 1..87 from Franklin T. Adams-Watters)
FORMULA
A351320(n) * a(n) = 1.a(n).1 where "." stands for concatenation. - Bernard Schott, Feb 07 2022
EXAMPLE
77 is a member since 1771 is a multiple of 77 (77*23).
MATHEMATICA
f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[1, 14] (* Ray Chandler, May 11 2007 *)
PROG
(PARI) A116436(k) = {local(l, d, lb, ub); d=divisors(10^(k+1)+1); l=[]; lb=10^(k-1); ub=10*lb; for(i=1, #d, if(d[i]>=lb&&d[i]<ub, l=concat(l, [d[i]]))); l}
l=[]; for(i=1, 60, l=concat(l, A116436(i))); l
\\ Franklin T. Adams-Watters, Apr 22 2008
(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
yield 1
for k in count(2):
t = 10**(k+1) + 1
yield from (t//i for i in range(100, 10, -1) if t%i == 0)
print(list(islice(agen(), 25))) # Michael S. Branicky, Mar 26 2023 following Franklin T. Adams-Watters but removing factorization
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Giovanni Resta, Feb 15 2006
STATUS
approved