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 A121861 Least previously nonoccurring positive integer such that partial sum + 1 is prime. 4
 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, 38, 60, 48, 58, 56, 54, 40, 50, 64, 68, 72, 76, 84, 66, 96, 74, 70, 80, 100, 86, 78, 88, 104, 90, 106, 122, 112, 98, 102, 94, 92, 118, 114, 108, 110, 124, 116, 138, 82, 120, 128, 150 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: 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, ...,. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = MIN{k>0 such that 1 + k + SUM[i=1..n-1]a(i) is prime and k <> a(i)}. EXAMPLE a(1) = 1 because 1+1 = 2 is prime. a(2) = 3 because 1+3+1 = 5 is prime. a(3) = 2 because 1+3+2+1 = 7 is prime. a(4) = 4 because 1+3+2+4+1 = 11 is prime. MAPLE N:= 200: # to get all terms before the first term > N A:= 1: A:= 3: P:= 5; S:= [seq(2*i, i=1..N/2)]: for n from 3 while assigned(A[n-1]) do   for k from 1 to nops(S) do     if isprime(P+S[k]) then       A[n]:= S[k];       P:= P + S[k];       S:= subsop(k=NULL, S);       break     fi   od; od: seq(A[i], i=1..n-2); # Robert Israel, May 02 2017 MATHEMATICA 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 *) CROSSREFS Cf. A000040, A121862. Sequence in context: A114745 A039915 A085346 * A317736 A060006 A123097 Adjacent sequences:  A121858 A121859 A121860 * A121862 A121863 A121864 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Aug 30 2006 EXTENSIONS Corrected and extended by Robert G. Wilson v, Aug 31 2006 Comment edited by Robert Israel, May 02 2017 STATUS approved

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Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)