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A248153
Start with a(0)=10, then a(n) = 7 times the n-th digit of the sequence.
1
10, 7, 0, 49, 0, 28, 63, 0, 14, 56, 42, 21, 0, 7, 28, 35, 42, 28, 14, 14, 7, 0, 49, 14, 56, 21, 35, 28, 14, 14, 56, 7, 28, 7, 28, 49, 0, 28, 63, 7, 28, 35, 42, 14, 7, 21, 35, 14, 56, 7, 28, 7, 28, 35, 42, 49, 14, 56, 49, 14, 56, 28, 63, 0, 14, 56, 42, 21, 49, 14, 56, 21, 35
OFFSET
0,1
COMMENTS
This sequence was inspired by E. Angelini's post to the SeqFan list, cf. links.
a(0)=10 is the smallest possible choice to ensure that the digit 0 appears anywhere in the sequence. a(0)=1 would lead to the same sequence with the terms 0 removed.
By construction, all terms a(n), n>0, are divisible by 7, and a(n)/7 yields the sequence of digits of the (concatenated) terms of this sequence.
It is easy to show that the distance between two 0's is strictly increasing from one occurrence to the next one. Thus, the asymptotic density of terms and/or digits 0 is zero, and the sequence can never "enter a loop".
LINKS
PROG
(PARI) a(n, s=10, m=7, d=[])={for(i=1, n, print1(s", "); d=concat(d, if(s, digits(s))); s=m*d[1]; d=vecextract(d, "^1")); s}
(Python)
def aupton(nn):
alst, astr = [10], "X10"
for n in range(1, nn+1):
alst.append(7 * int(astr[n]))
astr += str(alst[-1])
return alst
print(aupton(72)) # Michael S. Branicky, Oct 07 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Oct 02 2014
STATUS
approved