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%I #57 Jun 11 2023 23:29:10
%S 1,2,3,5,11,17,37,67,131,257,521,1031,2053,4099,8209,16411,32771,
%T 65537,131101,262147,524309,1048583,2097169,4194319,8388617,16777259,
%U 33554467,67108879,134217757,268435459,536870923,1073741827,2147483659
%N a(0)=1; for n > 0, a(n) = next prime after 2^(n-1).
%C Equals {1} union A014210. Unlike A014210, every positive integer can be written in one or more ways as a sum of terms of this sequence. See A203075, A203076.
%H M. F. Hasler & Bill McEachen, <a href="/A203074/b203074.txt">Table of n, a(n) for n = 0..1300</a> (missing lines n = 1159..1165 from Bill McEachen)
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Complete_sequence">"Complete" sequence</a>. [Wikipedia calls a sequence "complete" (sic) if every positive integer is a sum of distinct terms. This name is extremely misleading and should be avoided. - _N. J. A. Sloane_, May 20 2023]
%F A203074(n) = 2^(n-1) + A013597(n-1), for n > 0. - _M. F. Hasler_, Mar 15 2012
%F a(n) = A104080(n-1) for n > 2. - _Georg Fischer_, Oct 23 2018
%e a(5) = 17, since this is the next prime after 2^(5-1) = 2^4 = 16.
%t nextprime[n_Integer] := (k=n+1;While[!PrimeQ[k], k++];k); aprime[m_Integer] := (If[m==0, 1, nextprime[2^(m-1)]]); Table[aprime[l], {l,0,100}]
%t nxt[{n_,a_}]:={n+1,NextPrime[2^n]}; NestList[nxt,{0,1},40][[All,2]] (* _Harvey P. Dale_, Oct 10 2017 *)
%o (PARI) a(n)=if(n,nextprime(2^n/2+1),1) \\ _Charles R Greathouse IV_
%o (PARI) A203074(n)=nextprime(2^(n-1)+1)-!n \\ _M. F. Hasler_, Mar 15 2012
%o (Magma) [1] cat [NextPrime(2^(n-1)): n in [1..40]]; // _Vincenzo Librandi_, Feb 23 2018
%Y Cf. A013632, A013597, A014210, A104080, A203075, A203076.
%K nonn
%O 0,2
%A _Frank M Jackson_ and _N. J. A. Sloane_, Dec 28 2011.