A262138 Interleaved first and second differences of the prime numbers.

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

Offset: 1

Author

Reinhard Zumkeller, Sep 12 2015

Keywords

• sign

Comments

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

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

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

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

Examples

			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
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A036263, A001223, A000040.

Cf. A064113.

Programs

Haskell

import Data.List (transpose)
a262138 n = a262138_list !! (n-1)
a262138_list = concat $ transpose [a001223_list, a036263_list]

Mathematica

With[{nn=50},Riffle[Differences[Prime[Range[nn]]],Differences[ Prime[ Range[ nn]],2]]] (* Harvey P. Dale, Nov 01 2015 *)