A070218 a(1) = 2; a(n) is the smallest prime greater than the sum of all previous terms.

2, 3, 7, 13, 29, 59, 127, 241, 487, 971, 1949, 3889, 7789, 15569, 31139, 62297, 124577, 249181, 498331, 996689, 1993357, 3986711, 7973419, 15946841, 31893713, 63787391, 127574789, 255149591, 510299171, 1020598339, 2041196683, 4082393387, 8164786771, 16329573527

Offset: 1

Author

Amarnath Murthy, May 01 2002

Keywords

• nonn

Comments

Grows exponentially: ceiling(log_2(a(n))) = n. - Labos Elemer, May 08 2002

Links

• Vojtech Strnad, Table of n, a(n) for n = 1..2000 (first 200 terms from Zak Seidov)

Crossrefs

Cf. A063807, A151800.

Programs

Maple

s:= proc(n) option remember; `if`(n<1, 0, s(n-1)+a(n)) end:
a:= proc(n) option remember; `if`(n<1, 0, nextprime(s(n-1))) end:
seq(a(n), n=1..35);  # Alois P. Heinz, Sep 21 2021

Mathematica

tb[0]={} tb[x_] := Union[tb[x-1], m[x]] m[x_] := {Prime[1+PrimePi[Apply[Plus, tb[x-1]]]]} Flatten[Table[m[w], {w, 1, 10}]] (* Labos Elemer, May 08 2002 *)
bb={2};s=2;Do[p=Prime[PrimePi[s]+1];s=s+p;bb=Append[bb, p], {k, 32}];bb (Seidov)
Nest[Append[#,NextPrime[Total[#]]]&,{2},30] (* Zak Seidov, Oct 28 2011 *)

PARI

print1(s=2);for(n=2,99,print1(", "t=nextprime(s+1));s+=t)

Python

from sympy import nextprime
def aupton(terms):
    alst, s = [2], 2
    while len(alst) < terms:
        p = nextprime(s)
        alst.append(p)
        s += p
    return alst
print(aupton(31)) # Michael S. Branicky, Sep 21 2021

Extensions

More terms from Labos Elemer, May 08 2002

Corrected by Zak Seidov, May 21 2005