A219606 -id:A219606 - cp's OEIS frontend

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

Omar E. Pol, Nov 11 2007

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

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

Cf. A219606.

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

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

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

A340202 Primes followed by the difference from the next prime calculated by adding the digits of the lexicographically earliest distinct term.

Original entry on oeis.org

2, 1, 3, 20, 5, 110, 7, 4, 11, 200, 13, 22, 17, 1001, 19, 40, 23, 6, 29, 1010, 31, 15, 37, 112, 41, 1100, 43, 121, 47, 24, 53, 33, 59, 2000, 61, 42, 67, 130, 71, 10001, 73, 51, 79, 202, 83, 60, 89, 8, 97, 220, 101, 10010, 103, 301, 107, 10100, 109, 310, 113

Offset: 1

Carole Dubois, Dec 31 2020

			Prime 2 + (1) = prime 3;
prime 3 + (2+0) = prime 5;
prime 5 + (1+1+0) = prime 7;
prime 7 + (4) = prime 11;
prime 11 + (2+0+0) = prime 13;
prime 13 + (2+2) = 17; etc.

Cf. A000040 (primes), A219606.

Differences between consecutive primes: A001223, A134735, A340063.

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A134735 Primes followed by the difference from the next prime.

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A340202 Primes followed by the difference from the next prime calculated by adding the digits of the lexicographically earliest distinct term.

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