A083237 First order recursion: a(0)=5; a(n)=prime(n)-a(n-1).

5, -3, 6, -1, 8, 3, 10, 7, 12, 11, 18, 13, 24, 17, 26, 21, 32, 27, 34, 33, 38, 35, 44, 39, 50, 47, 54, 49, 58, 51, 62, 65, 66, 71, 68, 81, 70, 87, 76, 91, 82, 97, 84, 107, 86, 111, 88, 123, 100, 127, 102, 131, 108, 133, 118, 139, 124, 145, 126, 151, 130, 153, 140, 167, 144, 169, 148, 183, 154, 193, 156, 197, 162, 205, 168, 211, 172

Offset: 0

Author

Labos Elemer, Apr 23 2003

Keywords

• sign

Comments

Same function as in A083236 but initial value = 5.

Crossrefs

Cf. A000040, A001223.

Programs

Maple

A083237 := proc(n)
    option remember ;
    if n = 0 then
        5 ;
    else
        ithprime(n)-procname(n-1) ;
    end if;
end proc:
seq(A083237(n),n=0..100) ; # R. J. Mathar, Jun 20 2021

Mathematica

RecursionLimit$=10000; f[x_] := Prime[x]-f[x-1]; f[0]=5; Table[f[w], {w, 1, 100}]

Formula

Same implicit relationship: a(n-1)+a(n)=prime(n), the n-th prime;

It follows also that A001223(n)=a(n+1)-a(n-1).

Extensions

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