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

1,1

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)

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 *)

Prog

(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

Crossrefs

Cf. A063807, A151800.

Sequence in context: A199582 A255516 A113884 * A048456 A333313 A262829

Adjacent sequences: A070215 A070216 A070217 * A070219 A070220 A070221

Keyword

nonn

Author

Amarnath Murthy, May 01 2002

Extensions

More terms from Labos Elemer, May 08 2002

Corrected by Zak Seidov, May 21 2005

Status

approved