A121861 Least previously nonoccurring positive integer such that partial sum + 1 is prime.

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

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]:= 1: A[2]:= 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: A361379 A039915 A085346 * A338213 A317736 A060006

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