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

%I A083236 #21 Nov 07 2022 13:45:49
%S A083236 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,
%T A083236 50,51,52,55,54,59,68,63,74,65,84,67,90,73,94,79,100,81,110,83,114,85,
%U A083236 126,97,130,99,134,105,136,115,142,121,148,123,154,127,156,137,170,141,172,145
%N A083236 First order recursion: a(0)=2; a(n) = prime(n) - a(n-1).
%H A083236 Seiichi Manyama, <a href="/A083236/b083236.txt">Table of n, a(n) for n = 0..10000</a>
%F A083236 a(n-1) + a(n) = prime(n).
%F A083236 a(n+1)-a(n-1) = A001223(n).
%e A083236 n=6: a(6)+a(7) = 7+10 = prime(7) = 17 and a(7)+a(8) = 10+9 = 19 = prime(8);
%p A083236 A083236 := proc(n)
%p A083236     option remember ;
%p A083236     if n = 0 then
%p A083236         2 ;
%p A083236     else
%p A083236         ithprime(n)-procname(n-1) ;
%p A083236     end if;
%p A083236 end proc:
%p A083236 seq(A083236(n),n=0..100) ; # _R. J. Mathar_, Jun 20 2021
%t A083236 RecursionLimit$=10000; f[x_] := Prime[x]-f[x-1]; f[0]=2; Table[f[w], {w, 1, 100}]
%t A083236 Join[{0},Abs[Accumulate[Table[Prime[n](-1)^n,{n,2,70}]]]] (* _Harvey P. Dale_, Nov 20 2013 *)
%o A083236 (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
%Y A083236 Cf. A000040, A001223.
%K A083236 nonn
%O A083236 0,1
%A A083236 _Labos Elemer_, Apr 23 2003
%E A083236 a(0) prepended. - _R. J. Mathar_, Jun 20 2021