[seqfan] Re: Sum of a(n-1) and a(n)'s first digit
Eric Angelini
Eric.Angelini at kntv.be
Wed Nov 6 16:28:40 CET 2013
Hello SeqFans,
Lars has found some fascinating patterns -- see here:
http://www.cetteadressecomportecinquantesignes.com/FirstDigit.htm
Many thanks to Lars.
Best,
É.
-----Ursprungligt meddelande-----
From: Eric Angelini
Sent: Monday, November 04, 2013 5:22 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Sum of a(n-1) and a(n)'s first digit
Hello Seqfans,
let a(n) be the sum of a(n-1) and a(n)'s first digit.
Example : a(n-1) = 597
a(n) = 603 (as 597 + 6 = 603)
This doesn't work sometimes:
Example : a(n-1) = 991
a(n) = ?
Is there an infinite such sequence?
If you start the sequence with 0,9,... you might be
stuck: ..., 68, 75, 83, 92, ?
But there is a way to jump over 100: simply select this
branch:
0,9,10,11,12,13,14,15,16,17,18,20,22,...
instead of:
0,9,10,11,12,13,14,15,16,17,18,19,21,...
The first branch leads to ..., 68, 75, 83, 92.
The second one to ... 54, 60, 66, 73, 81, 90, 99, 100, 101, ...
Best,
É.
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