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A262138
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Interleaved first and second differences of the prime numbers.
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2
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1, 1, 2, 0, 2, 2, 4, -2, 2, 2, 4, -2, 2, 2, 4, 2, 6, -4, 2, 4, 6, -2, 4, -2, 2, 2, 4, 2, 6, 0, 6, -4, 2, 4, 6, -2, 4, -2, 2, 4, 6, -2, 4, 2, 6, 2, 8, -4, 4, -2, 2, 2, 4, -2, 2, 2, 4, 10, 14, -10, 4, 2, 6, -4, 2, 8, 10, -8, 2, 4, 6, 0, 6, -2, 4, 2, 6, 0, 6
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OFFSET
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1,3
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COMMENTS
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a(2*n-1) = prime(n+1) - prime(n);
a(2*n) = prime(n+2) - 2*prime(n+1) + prime(n);
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LINKS
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EXAMPLE
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A000040: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53
A001223: 1 2 2 4 2 4 2 4 6 2 6 4 2 4 6
A036263: 1 0 2 -2 2 -2 2 2 -4 4 -2 -2 2 2 0
A262138: 1 1 2 0 2 2 4 -2 2 2 4 -2 2 2 4 2 6 -4 2 4 6 -2 4 -2 2 2 4 2 6 0
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MATHEMATICA
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With[{nn=50}, Riffle[Differences[Prime[Range[nn]]], Differences[ Prime[ Range[ nn]], 2]]] (* Harvey P. Dale, Nov 01 2015 *)
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PROG
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(Haskell)
import Data.List (transpose)
a262138 n = a262138_list !! (n-1)
a262138_list = concat $ transpose [a001223_list, a036263_list]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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