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A275017
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a(1)=1, a(2)=2, a(n) = prime(n-2) - a(n-2) for n > 2.
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2
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1, 2, 1, 1, 4, 6, 7, 7, 10, 12, 13, 17, 18, 20, 23, 23, 24, 30, 35, 31, 32, 40, 41, 39, 42, 50, 55, 51, 48, 56, 61, 57, 66, 74, 71, 65, 78, 86, 79, 77, 88, 96, 91, 85, 100, 108, 97, 91, 114, 132, 113, 97, 120, 142, 121, 109, 136, 154, 133, 117, 144, 164, 139
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OFFSET
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1,2
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COMMENTS
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A plot of a(n) vs. n for n = 1..2000 (see the first plot under Links) shows that each of the points apparently falls onto one of four threads that weave back and forth among each other. "Zooming out" to view the first 30000 points results in a plot in which the threads are too close together to be easily distinguishable, but plotting a(n) - 6n vs. n (since all four threads lie fairly near a line of slope 6.0 from n = 0 to about n = 40000) makes it easier to observe the structure of the threads (see the second plot under Links). - Jon E. Schoenfield, Nov 20 2016
The four "threads" correspond a(n) for n in the four congruence classes mod 4. Note that a(n+4)-a(n)=prime(n+2)-prime(n), which might typically be small compared to the differences between a(n),a(n+1),a(n+2) and a(n+3). - Robert Israel, Nov 22 2016
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LINKS
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MAPLE
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A[1]:= 1: A[2]:= 2:
for n from 3 to 1000 do A[n]:= ithprime(n-2)-A[n-2] od:
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MATHEMATICA
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a = {1, 2}; Do[AppendTo[a, Prime[n - 2] - a[[n - 2]]], {n, 3, 63}]; a (* Michael De Vlieger, Nov 21 2016 *)
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PROG
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(Magma)
a:=[1, 2]; for n in [3..63] do a[n]:=NthPrime(n-2)-a[n-2]; end for; a; // Jon E. Schoenfield, Nov 20 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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