%I #11 Nov 01 2015 23:57:58

%S 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,

%T -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,

%U 4,2,6,-4,2,8,10,-8,2,4,6,0,6,-2,4,2,6,0,6

%N Interleaved first and second differences of the prime numbers.

%C a(2*n-1) = A001223(n); a(2*n) = A036263(n+2);

%C a(2*n-1) = prime(n+1) - prime(n);

%C a(2*n) = prime(n+2) - 2*prime(n+1) + prime(n);

%C a(2*A064113(n)) = 0.

%H Reinhard Zumkeller, <a href="/A262138/b262138.txt">Table of n, a(n) for n = 1..10000</a>

%e A000040: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53

%e A001223: 1 2 2 4 2 4 2 4 6 2 6 4 2 4 6

%e A036263: 1 0 2 -2 2 -2 2 2 -4 4 -2 -2 2 2 0

%e 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

%t With[{nn=50},Riffle[Differences[Prime[Range[nn]]],Differences[ Prime[ Range[ nn]],2]]] (* _Harvey P. Dale_, Nov 01 2015 *)

%o (Haskell)

%o import Data.List (transpose)

%o a262138 n = a262138_list !! (n-1)

%o a262138_list = concat $ transpose [a001223_list, a036263_list]

%Y Cf. A036263, A001223, A000040.

%Y Cf. A064113.

%K sign

%O 1,3

%A _Reinhard Zumkeller_, Sep 12 2015