[seqfan] Neighbors sum to a prime -- and odd ranks in T.
Eric Angelini
Eric.Angelini at kntv.be
Tue Oct 21 23:36:39 CEST 2014
Hello SeqFans,
T is the lexically first sequence with
no duplicates, such that a(n)+a(n+1)
is a prime = a(2n-1)
T = 2,0,3,4,7,6,11,18,13,24,17,30,29,42,31,52,37,60,41,20,47,80,59,92,71,36,73,84,83,48,99,102,97,96,101,150,61,162,67,112,127,130,139,...
Take n=1, then:
a(n)=a(1)=2
a(n+1)=a(2)=0
a(2n-1)=a(1)=2 and 2+0 is indeed 2, a prime
Take n=6, then:
a(n)=a(6)=6
a(n+1)=a(7)=11
a(2n-1)=a(11)=17 and 6+11 is indeed 17, a prime
Take n=21, then:
a(n)=a(21)=47
a(n+1)=a(22)=80
a(2n-1)=a(41)=127 and 47+80 is indeed 127, a prime
I'm quite confident that all even numbers
will show sooner or later in T.
Best,
É.
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