[seqfan] Re: puzzled by A082945, definition of rev n
Maximilian Hasler
maximilian.hasler at gmail.com
Fri Apr 17 19:52:39 CEST 2009
>> The aim is to extend
>> http://www.research.att.com/~njas/sequences/A082946
A082946 Palindromes satisfying A082945.
well, if (rev n) is the reversal of the last #n digits of a(i), then
any (odd digit) palindrome with middle digit 1 is in A082945 and
A082946.
The nontrivial elements would rather be the non-palindromic terms of A082945.
OTOH, for more than 3 digits, the sequence would soon be "flooded" by
numbers satisfying the definition using only very few digits from the
start.
Specifically, if
amb is in the sequence, with a = m * b
(m=middle digit, b = "rev a") then any
axmyb is in the sequence with x,y having the same number of digits.
So one could impose that n must be all that precedes the middle digit
and "rev n" = [reversal of] all that follows the middle digit
(w/ or w/o allowing leading zeroes)
Remark: according to the current "definition", the number 1 should
also be in A082945 and A082946.
Maximilian
PS: IMHO these sequences are not extremely interesting...
On Fri, Apr 17, 2009 at 1:25 PM, Maximilian Hasler
<maximilian.hasler at gmail.com> wrote:
> A082945 Numbers starting with n such that n/(rev n) is the center
> digit, where (rev n) is the reverse of n.
> 111, 212, 221, 313, 331, 414, 422, 441, 515, 551, 616, 623, 632, 661,
> 717, 771, 818, 824, 842, 881, 919, 933, 991
>
> I think here it (rev n) means the last digit when n is the first digit
> and probably the reversal of the last k digits when n are the first k digits.
> (A priori any positive k <= number of digits of a(m) seems allowed.)
>
> Maximilian
>
> On Fri, Apr 17, 2009 at 1:01 PM, Richard Mathar
> <mathar at strw.leidenuniv.nl> wrote:
>>
>> I am wondering what the definition of
>> http://www.research.att.com/~njas/sequences/A082945
>> might actually be. What does (rev n) mean, given the example that
>> for the a(12) entry, n=6 is associated with rev n=2. I am only familiar
>> with digit reversion equivalent to reading numbers from right to left,
>> so a single-digit number is the same as its reversion, as in A004086.
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