

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
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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..n1]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[n1]) 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..n2); # 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



