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A061535 a(n) = a(n-1) + the number of primes <= a(n-1).

%I A061535 #20 Jun 18 2021 09:12:59
%S A061535 2,3,5,8,12,17,24,33,44,58,74,95,119,149,184,226,274,332,399,477,568,
%T A061535 671,792,930,1088,1269,1474,1707,1973,2271,2608,2986,3415,3895,4434,
%U A061535 5036,5710,6461,7299,8229,9260,10407,11681,13083,14639,16354,18250
%N A061535 a(n) = a(n-1) + the number of primes <= a(n-1).
%C A061535 From _Robert G. Wilson v_, Jan 14 2012: (Start)
%C A061535 Obviously, the first difference is PrimePi(a(n)).
%C A061535 Number of terms less than and equal to 2^k: 1, 2, 4, 5, 7, 10, 13, 16, 20, 24, 29, 34, 39, 46, 52, 59, 67, 75, 83, 92, 101, 111, 122, 132, 144, 156, 168, 181, 194, 208, 222, 237, 252, 268, 284, 301, 318, 335, 353, 372, 391, 411, 431, 451, 472, 494, 516, 538, ....
%C A061535 Number of terms less than 10^k: 4, 12, 24, 41, 64, 91, 124, 163, 206, 255, 310, 369, 434, 505, .... (End)
%H A061535 Robert G. Wilson v, <a href="/A061535/b061535.txt">Table of n, a(n) for n = 1..535</a> (first 300 terms from T. D. Noe)
%p A061535 A061535 := proc(n)
%p A061535     option remember;
%p A061535     if n= 1 then
%p A061535         2;
%p A061535     else
%p A061535         procname(n-1)+numtheory[pi](procname(n-1)) ;
%p A061535     end if;
%p A061535 end proc:
%p A061535 seq(A061535(n),n=1..30); # _R. J. Mathar_, Jun 18 2021
%t A061535 a[1] = 2; a[n_] := a[n] = a[n - 1] + PrimePi[ a[n - 1] ]; Table[ a[n], {n, 1, 75} ]
%t A061535 NestList[#+PrimePi[#]&,2,50] (* _Harvey P. Dale_, Apr 15 2019 *)
%o A061535 (PARI) { default(primelimit, 4294965247); for (n=1, 238, if (n==1, a=2, a+=primepi(a)); write("b061535.txt", n, " ", a) ) } \\ _Harry J. Smith_, Jul 24 2009
%K A061535 nonn
%O A061535 1,1
%A A061535 _R. K. Guy_, _Robert G. Wilson v_, May 14 2001