A083236 First order recursion: a(0)=2; a(n) = prime(n) - a(n-1).

2, 0, 3, 2, 5, 6, 7, 10, 9, 14, 15, 16, 21, 20, 23, 24, 29, 30, 31, 36, 35, 38, 41, 42, 47, 50, 51, 52, 55, 54, 59, 68, 63, 74, 65, 84, 67, 90, 73, 94, 79, 100, 81, 110, 83, 114, 85, 126, 97, 130, 99, 134, 105, 136, 115, 142, 121, 148, 123, 154, 127, 156, 137, 170, 141, 172, 145

Offset: 0

Author

Labos Elemer, Apr 23 2003

Keywords

• nonn

Examples

			n=6: a(6)+a(7) = 7+10 = prime(7) = 17 and a(7)+a(8) = 10+9 = 19 = prime(8);
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000040, A001223.

Programs

Maple

A083236 := proc(n)
    option remember ;
    if n = 0 then
        2 ;
    else
        ithprime(n)-procname(n-1) ;
    end if;
end proc:
seq(A083236(n),n=0..100) ; # R. J. Mathar, Jun 20 2021

Mathematica

RecursionLimit$=10000; f[x_] := Prime[x]-f[x-1]; f[0]=2; Table[f[w], {w, 1, 100}]
Join[{0},Abs[Accumulate[Table[Prime[n](-1)^n,{n,2,70}]]]] (* Harvey P. Dale, Nov 20 2013 *)

PARI

lista(nn) = {my(last = 2, new, v=vector(nn)); for (n=1, nn, v[n] = prime(n) - last; last = v[n];); v;} \\ Michel Marcus, Mar 27 2020

Formula

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

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

Extensions

a(0) prepended. - R. J. Mathar, Jun 20 2021