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

%I A083237 #12 Jun 20 2021 09:57:45
%S A083237 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 A083237 50,47,54,49,58,51,62,65,66,71,68,81,70,87,76,91,82,97,84,107,86,111,
%U A083237 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 A083237 First order recursion: a(0)=5; a(n)=prime(n)-a(n-1).
%C A083237 Same function as in A083236 but initial value = 5.
%F A083237 Same implicit relationship: a(n-1)+a(n)=prime(n), the n-th prime;
%F A083237 It follows also that A001223(n)=a(n+1)-a(n-1).
%p A083237 A083237 := proc(n)
%p A083237     option remember ;
%p A083237     if n = 0 then
%p A083237         5 ;
%p A083237     else
%p A083237         ithprime(n)-procname(n-1) ;
%p A083237     end if;
%p A083237 end proc:
%p A083237 seq(A083237(n),n=0..100) ; # _R. J. Mathar_, Jun 20 2021
%t A083237 RecursionLimit$=10000; f[x_] := Prime[x]-f[x-1]; f[0]=5; Table[f[w], {w, 1, 100}]
%Y A083237 Cf. A000040, A001223.
%K A083237 sign
%O A083237 0,1
%A A083237 _Labos Elemer_, Apr 23 2003
%E A083237 a(0) preprended. - _R. J. Mathar_, Jun 20 2021