A123128 Add n to the n-th difference between consecutive primes.

2, 4, 5, 8, 7, 10, 9, 12, 15, 12, 17, 16, 15, 18, 21, 22, 19, 24, 23, 22, 27, 26, 29, 32, 29, 28, 31, 30, 33, 44, 35, 38, 35, 44, 37, 42, 43, 42, 45, 46, 43, 52, 45, 48, 47, 58, 59, 52, 51, 54, 57, 54, 63, 60, 61, 62, 59, 64, 63, 62, 71, 76, 67, 66, 69, 80, 73, 78, 71, 74, 77

Offset: 1

Author

Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 30 2006

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• A. Frank & P. Jacqueroux, International Contest, 2001. Item 20.

Crossrefs

Cf. A000040 (primes), A001223, A014689, A014690, A095116.

Programs

Magma

[n + NthPrime(n+1) - NthPrime(n): n in [1..80]]; // G. C. Greubel, Aug 03 2021

Mathematica

With[{nn=80},Total/@Thread[{Differences[Prime[Range[nn]]],Range[nn-1]}]] (* Harvey P. Dale, Jun 02 2014 *)

PARI

for(n=1,100,print1(prime(n+1)-prime(n)+n,","))

Sage

[n + nth_prime(n+1) - nth_prime(n) for n in (1..80)] # G. C. Greubel, Aug 03 2021

Formula

a(n) = n + (prime(n+1) - prime(n)) = n + A001223(n).

From G. C. Greubel, Aug 03 2021: (Start)

a(n) = A014690(n) - prime(n) = A095116(n+1) - prime(n).

a(n) = prime(n+1) - A014689(n). (End)