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A083237 First order recursion: a(0)=5; a(n)=prime(n)-a(n-1). 3

%I

%S 5,-3,6,-1,8,3,10,7,12,11,18,13,24,17,26,21,32,27,34,33,38,35,44,39,

%T 50,47,54,49,58,51,62,65,66,71,68,81,70,87,76,91,82,97,84,107,86,111,

%U 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

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

%C Same function as in A083236 but initial value = 5.

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

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

%p A083237 := proc(n)

%p option remember ;

%p if n = 0 then

%p 5 ;

%p else

%p ithprime(n)-procname(n-1) ;

%p end if;

%p end proc:

%p seq(A083237(n),n=0..100) ; # _R. J. Mathar_, Jun 20 2021

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

%Y Cf. A000040, A001223.

%K sign

%O 0,1

%A _Labos Elemer_, Apr 23 2003

%E a(0) preprended. - _R. J. Mathar_, Jun 20 2021

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Last modified August 14 05:20 EDT 2022. Contains 356110 sequences. (Running on oeis4.)