%I #24 Jun 06 2021 02:54:02

%S 2,1,4,6,10,8,12,16,14,24,30,22,18,26,34,36,20,28,38,40,32,42,46,48,

%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(n) = smallest positive integer not already in sequence such that the partial sum a(1)+...+a(n) is prime.

%C 1 is the only odd number in this sequence. - _Derek Orr_, Feb 07 2015

%C Conjecture: Every even numbers appears. - _N. J. A. Sloane_, May 29 2017

%H Chai Wah Wu, <a href="/A054408/b054408.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..4100 from N. J. A. Sloane).

%t t = {2}; Do[i = 1; While[! PrimeQ[Total[t] + i] || MemberQ[t, i], i++]; AppendTo[t, i], {65}]; t (* _Jayanta Basu_, Jul 04 2013 *)

%o (PARI) v=[2];n=1;while(n<100,if(isprime(vecsum(v)+n)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ _Derek Orr_, Feb 07 2015

%o (Python)

%o from sympy import isprime

%o def aupton(terms):

%o alst, aset, asum = [], set(), 0

%o while len(alst) < terms:

%o an = 1

%o while True:

%o while an in aset: an += 1

%o if isprime(asum + an):

%o alst, aset, asum = alst + [an], aset | {an}, asum + an

%o break

%o an += 1

%o return alst

%o print(aupton(66)) # _Michael S. Branicky_, Jun 05 2021

%Y Cf. A254337.

%Y See A073659 for another version.

%Y In A055265 only pairs of adjacent terms add to primes.

%K nonn,easy

%O 1,1

%A _Henry Bottomley_, May 09 2000