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A093502 a(1) = 2; for n > 0, a(n+1) is the a(n)-th prime after a(n).

%I A093502 #41 Nov 02 2024 12:45:43
%S A093502 2,5,19,103,733,6691,76831,1081429,18242699,361919671,8309068723,
%T A093502 217809953467,6445388418589,213232943658197,7821073506524401,
%U A093502 315743571062703689
%N A093502 a(1) = 2; for n > 0, a(n+1) is the a(n)-th prime after a(n).
%C A093502 With prepended a(0) = 1 this is the lexicographically earliest infinite sequence such that A056239(a(n)) = a(n-1) + A056239(a(n-1)). - _Antti Karttunen_, Nov 02 2024
%F A093502 a(n) = prime(pi(a(n-1)) + a(n-1)). - _Vladeta Jovovic_, Jun 19 2004
%F A093502 a(1)=2, a(n) = next a(n-1)th prime after a(n-1). - _Zak Seidov_, Mar 21 2009
%F A093502 a(n+1) = A000040(a(n) + index of a(n) in A000040). - _David James Sycamore_, Aug 20 2017
%F A093502 a(n) = A000040(A074271(n)), A056239(a(n)) = A074271(n). - _Antti Karttunen_, Nov 02 2024
%e A093502 19 follows 5 as there are 5 primes > 5 and up to 19 inclusive, (7,11,13,17,19).
%t A093502 a[1] := 2; a[n_] := Prime[PrimePi[a[n - 1]] + a[n - 1]]; Table[a[n], {n, 1, 10}] (* _Stefan Steinerberger_, Apr 10 2006 *)
%t A093502 NestList[Prime[PrimePi[ # ] + # ] &, 2, 13] (* _Zak Seidov_, Mar 21 2009 *)
%o A093502 (Python)
%o A093502 from sympy import prime
%o A093502 p, q = 2, 1
%o A093502 A093502_list = [p]
%o A093502 for _ in range(15):
%o A093502     r = p + q
%o A093502     p, q = prime(r), r
%o A093502     A093502_list.append(p) # _Chai Wah Wu_, Jun 17 2019
%Y A093502 Cf. A000040, A000720, A056239, A074271.
%K A093502 more,nonn
%O A093502 1,1
%A A093502 _Amarnath Murthy_, Apr 17 2004
%E A093502 a(10) from _Vladeta Jovovic_, Jun 19 2004
%E A093502 More terms from _Stefan Steinerberger_, Apr 10 2006
%E A093502 a(13) from _Zak Seidov_, Mar 21 2009
%E A093502 a(14)-a(15) from _Donovan Johnson_, Dec 08 2009
%E A093502 Better definition from _Jon E. Schoenfield_, Aug 22 2017
%E A093502 a(16) from _Chai Wah Wu_, Jun 17 2019