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%I #13 Nov 27 2021 16:20:29
%S 1,2,5,11,23,43,89,179,359,719,1433,2879,5749,11497,22993,45989,91997,
%T 183971,367949,735901,1471807,2943599,5887213,11774429,23548853,
%U 47097697,94195421,188390809,376781623,753563269,1507126519,3014253049
%N Smallest prime (or noncomposite) strictly greater than sum of previous terms (with a(0)=1).
%C 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.
%H Harry J. Smith, <a href="/A064934/b064934.txt">Table of n, a(n) for n=0..200</a>
%t 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
%t Module[{s={1}},Do[AppendTo[s,NextPrime[Total[s]]],{40}];s] (* _Harvey P. Dale_, Dec 29 2012 *)
%t nxt[{t_,a_}]:=Module[{c=NextPrime[t]},{t+c,c}]; NestList[nxt,{1,1},40][[All,2]] (* _Harvey P. Dale_, Nov 27 2021 *)
%o (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
%K nonn
%O 0,2
%A _Henry Bottomley_, Oct 26 2001
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