[seqfan] Re: Odd [resp. "even"] number as difference of its neighbours

[Lars Blomberg]

Hello,

T = 2,1,3,4,5,9,14,6,7,13,20,8,10,11,21,32,12,15,27,42,16,17,33,50,18,19,37,56,
22,23,45,68,24,25,49,74,26,28,29,57,86,30,31,61,92,34,35,69,104,36,38,39,77,
116,40,41,81,122,43,--165--,208,44,46,47,93,140,48,51,99,150,52,53,105,158,54,55,
109,164,58,59,117,176,60,62,63,125,188,64,65,129,194,66,67,133,200,70,71,141,
212,72,73,145,218,75,293,368,76,78,79,157,236,80,82,83,(165)
And 165 is already used.

Similarly
U = 1,2,3,4,7,5,6,11,8,--19--,9,10,(19)  and 19 is already used.

Several other small starting values meet the same fate.

Unlike the recent sequence where the condition applies to prime a(n) which
has generated 10^8 terms without conflict.

One could try backtracking and select a larger value than the smallest available for those terms that we are free to choose.

/Lars B

-----Ursprungligt meddelande-----
Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Eric Angelini
Skickat: den 23 januari 2016 11:34
Till: Sequence Discussion list <seqfan at list.seqfan.eu>
Ämne: [seqfan] Odd [resp. "even"] number as difference of its neighbours

Hello SeqFans,

T is the lexico-first permutation of
the integers > 0 such that every odd
term a(n) = a(n+1)-a(n-1)

T = 2,1,3,4,5,9,14,6,7,13,20,8,10,11,21,32,
12,15,27,42,16,17,33,50,18,19,37,56,22,
23,45,68,...

And U is the lexico-first permutation of the integers > 0 such that every even term a(n) = a(n+1)-a(n-1)

U = 1,2,3,4,7,5,6,11,8,19,9,10,29,12,41,
13,14,27,15,16,31,17,18,35,20,55,21,22,33,...

Best,
É.


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