Search: id:A064934
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%I A064934
%S A064934 1,2,5,11,23,43,89,179,359,719,1433,2879,5749,11497,22993,45989,91997,
%T A064934 183971,367949,735901,1471807,2943599,5887213,11774429,23548853,
%U A064934 47097697,94195421,188390809,376781623,753563269,1507126519,3014253049
%N A064934 Smallest prime (or non-composite) strictly greater than sum of previous 
               terms [with a(0)=1].
%C A064934 Seems to tend towards 2^(n+0.4891533...); replacing "prime" by "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 providing that the underlying 
               sequence is increasing but no faster than 2^n.
%H A064934 Harry J. Smith, <a href="b064934.txt">Table of n, a(n) for n=0,...,200</
               a>
%t A064934 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
%o A064934 (PARI) { for (n=0, 200, if (n, a=nextprime(s + 1); s+=a, a=s=1); write("b064934.txt", 
               n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Sep 29 2009]
%Y A064934 Sequence in context: A039693 A062475 A124920 this_sequence A005986 A147878 
               A140992
%Y A064934 Adjacent sequences: A064931 A064932 A064933 this_sequence A064935 A064936 
               A064937
%K A064934 nonn
%O A064934 0,2
%A A064934 Henry Bottomley (se16(AT)btinternet.com), Oct 26 2001

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