OFFSET
0,2
COMMENTS
Seems to tend towards 2^(n + 0.4891533...); replacing "prime" with "number" or "power of 2" and starting with a(0)=1, it would be 2^n; with primes starting with a(1)=2 but no a(0), it seems as if it could tend towards 2^(n - 0.07323...); while with squares starting with a(0)=0 it seems as if it would tend towards 2^(n + 0.4294...); it seems plausible that all such sequences have similar properties provided that the underlying sequence is increasing but no faster than 2^n.
LINKS
Harry J. Smith, Table of n, a(n) for n=0..200
MATHEMATICA
NextPrim[n_Integer] := Block[ {k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = {1}; Do[a = Append[a, NextPrim[ Apply[ Plus, a]]], {n, 1, 32} ]; a
Module[{s={1}}, Do[AppendTo[s, NextPrime[Total[s]]], {40}]; s] (* Harvey P. Dale, Dec 29 2012 *)
nxt[{t_, a_}]:=Module[{c=NextPrime[t]}, {t+c, c}]; NestList[nxt, {1, 1}, 40][[All, 2]] (* Harvey P. Dale, Nov 27 2021 *)
PROG
(PARI) { for (n=0, 200, if (n, a=nextprime(s + 1); s+=a, a=s=1); write("b064934.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 29 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Oct 26 2001
STATUS
approved