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A063807 a(0) = 0, a(n+1) = a(n) + next prime larger than a(n).

%I A063807 #24 Apr 25 2022 08:04:08
%S A063807 0,2,5,12,25,54,113,240,481,968,1939,3888,7777,15566,31135,62274,
%T A063807 124571,249148,498329,996660,1993349,3986706,7973417,15946836,
%U A063807 31893677,63787390,127574781,255149570,510299161,1020598332,2041196671,4082393354,8164786741,16329573512
%N A063807 a(0) = 0, a(n+1) = a(n) + next prime larger than a(n).
%H A063807 Alois P. Heinz, <a href="/A063807/b063807.txt">Table of n, a(n) for n = 0..2500</a> (first 201 terms from Harry J. Smith)
%e A063807 0 + 2 = 2, 2 + 3 = 5, 5 + 7 = 12, 12 + 13 = 25, 25 + 29 = 54, ...
%p A063807 a:= proc(n) option remember; `if`(n=0, 0, (t->
%p A063807       t+nextprime(t))(a(n-1)))
%p A063807     end:
%p A063807 seq(a(n), n=0..35);  # _Alois P. Heinz_, Sep 21 2021
%t A063807 Join[{0}, NestList[# + NextPrime[#] &, 2, 50]] (* Updated by _Jean-François Alcover_, Apr 25 2022 for a(0)=0 *)
%o A063807 (PARI) s(n)=if(n<1,n=0,s(n-1)+nextprime(s(n-1)+1)); for(n=0,21,print(s(n)))
%o A063807 (PARI) { for (n=0, 200, if (n, a+=nextprime(a + 1), a=0); write("b063807.txt", n, " ", a) ) } \\ _Harry J. Smith_, Aug 31 2009
%Y A063807 Cf. A070218, A151800.
%K A063807 nonn
%O A063807 0,2
%A A063807 Pedro Ortiz-Villajos (perico1(AT)erols.com), Aug 20 2001
%E A063807 More terms from _Harvey P. Dale_ and _Jason Earls_, Aug 20 2001