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%I #33 Jun 13 2021 09:01:46
%S 1,2,4,6,10,8,12,16,14,24,30,22,18,26,34,36,20,28,38,40,32,42,46,48,
%T 44,52,56,60,54,58,66,50,64,62,70,84,90,72,92,76,86,94,74,88,68,82,80,
%U 102,96,100,114,98,78,112,120,110,108,106,126,122,130,132,134,124,128,118
%N a(1) = 1; for n > 1, a(n) is the smallest even number not already in the sequence such that a(1) + ... + a(n) is a prime.
%C Essentially the same as A054408. - _R. J. Mathar_, Dec 15 2008
%C Conjecture: Every even number appears. - _N. J. A. Sloane_, May 29 2017
%H Chai Wah Wu, <a href="/A073659/b073659.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..4097 from N. J. A. Sloane).
%t t = {1}; Do[i = 2; While[! PrimeQ[Total[t] + i] || MemberQ[t, i], i += 2]; AppendTo[t, i], {65}]; t (* _Jayanta Basu_, Jul 04 2013 *)
%o (PARI) v=[1];n=1;while(n<200,if(isprime(n+vecsum(v))&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ _Derek Orr_, Jun 01 2015
%Y Cf. A054408, A073660.
%Y See A055265 for a version where the sums of two adjacent terms are primes.
%K nonn,easy
%O 1,2
%A _Amarnath Murthy_, Aug 10 2002
%E More terms from _Sascha Kurz_, Jan 28 2003
%E Offset corrected by _Chai Wah Wu_, Aug 27 2017
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