A134735 Primes followed by the difference from the next prime.

2, 1, 3, 2, 5, 2, 7, 4, 11, 2, 13, 4, 17, 2, 19, 4, 23, 6, 29, 2, 31, 6, 37, 4, 41, 2, 43, 4, 47, 6, 53, 6, 59, 2, 61, 6, 67, 4, 71, 2, 73, 6, 79, 4, 83, 6, 89, 8, 97, 4, 101, 2, 103, 4, 107, 2, 109, 4, 113, 14, 127, 4, 131, 6, 137, 2

Offset: 1

Author

Omar E. Pol, Nov 11 2007

Keywords

• easy
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Crossrefs

Prime numbers: A000040. Differences between consecutive primes: A001223.

Cf. A219606.

Programs

Haskell

import Data.List (transpose)
a134735 n = a134735_list !! (n-1)
a134735_list = concat $ transpose [a000040_list, a001223_list]
-- Reinhard Zumkeller, Dec 12 2012

Mathematica

With[{pr=Prime[Range[40]]},Riffle[pr,Differences[pr]]] (* Harvey P. Dale, Jul 17 2020 *)

Formula

If n is odd then a(n) = A000040((n+1)/2) else a(n) = A001223(n/2).