Puzzle Sequence

[David Wilson]

----- Original Message ----- 
From: <jonscho at hiwaay.net>
To: <ralf at ark.in-berlin.de>; "Ralf Stephan" <ralf at ark.in-berlin.de>
Cc: "David Wilson" <davidwwilson at comcast.net>; "Sequence Fans" 
<seqfan at ext.jussieu.fr>
Sent: Tuesday, June 26, 2007 2:49 PM
Subject: Re: Puzzle Sequence


> Some observations about the terms thus far:
>
> At many (but not all) steps, the hundreds and ones digits are incremented 
> by 1
> and the tens digit is decremented by 1 (yielding a difference of 7*13=91).
>
> If a(n) is in the sequence, then so is a(n)+1001 (unless the latter is
> divisible by 10).  7*11*13=1001.

True for the small numbers you've seen, but stops being true at a(n) = 9240.

But you are on to something. Here's some encouragement:

a(n)+1001 is in the sequence if (not iff ) the addition does not cause a 
carry.


More precisely,

> If any a(n) is divisible by 10, then a(n)/10 is also in the sequence.

This is true.

> Quoting Ralf Stephan <ralf at ark.in-berlin.de>:
>
>> You wrote
>> > Additional elements:
>> >
>> > 0 56 147 238 329 560 651 742 798 833 889 924 1001 1057 1148 1239 1470
>>
>> > 1561 1652 1743 1799 1834 1925 2002 2058 2149 2380 2471 2562 2653 2744
>>
>> Well, the 1st differences so far consist of a sequence containing
>> only the numbers 7*5, 7*8, 7*11, 7*13, and 7*33.
>>
>>
>
>
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