A096379 a(n) = prime(n) + prime(n+1) - prime(n+2).

0, 1, 1, 5, 7, 11, 13, 13, 21, 23, 27, 35, 37, 37, 41, 51, 53, 57, 65, 65, 69, 73, 75, 85, 95, 97, 101, 103, 95, 109, 121, 129, 127, 137, 143, 145, 153, 157, 161, 171, 169, 179, 187, 191, 185, 187, 207, 221, 223, 223, 231, 229, 235, 245, 251, 261, 263, 267, 275, 271

Offset: 1

Author

Cino Hilliard, Aug 04 2004

Keywords

• nonn
• easy

Comments

Sequence is non-monotonic: see, e.g., a(29), a(33), and a(41). - Zak Seidov, Jan 21 2013

Ishikawa proved that a(n) > 0 for n > 1. - Jonathan Sondow, Feb 13 2014

Examples

			a(1) = prime(1) + prime(2) - prime(3) = 2 + 3 - 5 = 0.
a(25) = prime(25) + prime(26) - prime(27) = 97 + 101 - 103 = 95.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..5000 (terms 1..1000 from Zak Seidov)
• Heihachiro Ishikawa, Über die Verteilung der Primzahlen, Sci. Rep. Tokyo Bunrika Daigaku, Sect. A 2 (1934), 27-40.

Crossrefs

Cf. A000040, A001043, A001223.

Programs

Magma

[NthPrime(n)+NthPrime(n+1)-NthPrime(n+2):n in [1..60]]; //  Marius A. Burtea, Aug 17 2019

Maple

A096379 := proc(n)
    ithprime(n+1)+ithprime(n)-ithprime(n+2) ;
end proc:
seq(A096379(n),n=1..80) ; # R. J. Mathar, Sep 10 2016

Mathematica

#[[1]] + #[[2]] - #[[3]] & /@ Partition[Prime[Range[62]], 3, 1] (* Zak Seidov, Apr 09 2013 *)
ListConvolve[{-1,1,1},Prime[Range[100]]] (* Zak Seidov, Dec 03 2014 *)

PARI

g(n)=for(x=1,n,print1(prime(x)+prime(x+1)-prime(x+2)","))

PARI

first(n)=my(v=vector(n),p=2,q=3,k); forprime(r=5,, if(k++>n, break); v[k]=p+q-r; p=q; q=r); v \\ Charles R Greathouse IV, Oct 03 2017

Formula

a(n) = A001043(n) - A000040(n+2). - A.H.M. Smeets, Aug 17 2019

a(n) = A000040(n) - A001223(n+1). - Jon Maiga, Aug 17 2019

Extensions

Edited by Zak Seidov, Aug 27 2012

Definition reworded by N. J. A. Sloane, Aug 27 2012