%I A121861
%S A121861 1,3,2,4,6,12,8,10,14,18,22,26,24,16,30,32,28,20,34,36,42,44,46,62,52,
%T A121861 38,60,48,58,56,54,40,50,64,68,72,76,84,66,96,74,70,80,100,86,78,88,104,
%U A121861 90,106,122,112,98,102,94,92,118,114,108,110,124,116,138,82,120,128,150
%N A121861 Least previously nonoccurring positive integer such that partial sum 
               + 1 is prime.
%C A121861 a(n) = {1,3} UNION {permutation of even positive numbers}. The corresponding 
               partial sums + 1 are 2, 5, 7, 13, 17, 29, 37, 47, 61, 79, 101, 127, 
               151, ...,.
%F A121861 a(n) = MIN{k>0 such that 1 + k + SUM[i=1..n-1]a(i) is prime and k <> 
               a(i)}.
%e A121861 a(1) = 1 because 1+1 = 2 is prime.
%e A121861 a(2) = 3 because 1+3+1 = 5 is prime.
%e A121861 a(3) = 2 because 1+3+2+1 = 7 is prime.
%e A121861 a(4) = 4 because 1+3+2+4+1 = 11 is prime.
%t A121861 f[s_] := Append[s, k = 1; p = 1 + Plus @@ s; While[MemberQ[s, k] || ! 
               PrimeQ[p + k], k++ ]; k]; Nest[f, {}, 67] (* Robert G. Wilson v *)
%Y A121861 Cf. A000040, A121862.
%Y A121861 Sequence in context: A114745 A039915 A085346 this_sequence A060006 A123097 
               A134571
%Y A121861 Adjacent sequences: A121858 A121859 A121860 this_sequence A121862 A121863 
               A121864
%K A121861 easy,nonn
%O A121861 1,2
%A A121861 Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 30 2006
%E A121861 Corrected and extended by Robert G. Wilson v, Aug 31 2006