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

2, 3, 5, 8, 12, 17, 24, 33, 44, 58, 74, 95, 119, 149, 184, 226, 274, 332, 399, 477, 568, 671, 792, 930, 1088, 1269, 1474, 1707, 1973, 2271, 2608, 2986, 3415, 3895, 4434, 5036, 5710, 6461, 7299, 8229, 9260, 10407, 11681, 13083, 14639, 16354, 18250

Offset: 1

Author

R. K. Guy, Robert G. Wilson v, May 14 2001

Keywords

• nonn

Comments

From Robert G. Wilson v, Jan 14 2012: (Start)

Obviously, the first difference is PrimePi(a(n)).

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, ....

Number of terms less than 10^k: 4, 12, 24, 41, 64, 91, 124, 163, 206, 255, 310, 369, 434, 505, .... (End)

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..535 (first 300 terms from T. D. Noe)

Programs

Maple

A061535 := proc(n)
    option remember;
    if n= 1 then
        2;
    else
        procname(n-1)+numtheory[pi](procname(n-1)) ;
    end if;
end proc:
seq(A061535(n),n=1..30); # R. J. Mathar, Jun 18 2021

Mathematica

a[1] = 2; a[n_] := a[n] = a[n - 1] + PrimePi[ a[n - 1] ]; Table[ a[n], {n, 1, 75} ]
NestList[#+PrimePi[#]&,2,50] (* Harvey P. Dale, Apr 15 2019 *)

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