OFFSET
1,2
COMMENTS
a(n) = n only for n: 1, 2, 6, 12 for all n < 10000. - Robert G. Wilson v, Nov 21 2012
a(n) = ~(1 +- 2/5)*n. - Robert G. Wilson v, Nov 21 2012
a(n) is odd if and only if n == 1 (mod 3). - Robert Israel, Dec 09 2015
The odd terms grow according to a(3k+1) ~ 2k and the even terms according to a(n) ~ 4n/3. - M. F. Hasler, Dec 11 2015
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
After 8 and 6 the next term is 3 as 8+6+3 = 17 is a prime.
MAPLE
N:= 200: # to get all terms before the first > N
V:= Vector(N):
V[1]:= 1: V[2]:= 1:
A[1]:= 1: A[2]:= 2:
m0:= 3: m:= 0:
for n from 3 while m <= N do
t:= A[n-1]+A[n-2];
m1:= m0 + (m0+t+1 mod 2);
for m from m1 to N by 2 do if isprime(m+t) and V[m] = 0 then
A[n]:= m;
V[m]:= 1;
break;
fi od:
if m = m0 then
while m0 < N and V[m0] = 1 do m0:= m0+1 od:
fi;
od:
seq(A[j], j=1..n-2); # Robert Israel, Dec 09 2015
MATHEMATICA
f[s_List] := Block[{p = s[[-2]] + s[[-1]], q = 1}, While[ !PrimeQ[p + q] || MemberQ[s, q], q++]; Append[s, q]]; Nest[f, {1, 2}, 70] (* Robert G. Wilson v, Nov 21 2012 *)
PROG
(PARI) A076990(n, verbose=0/*=1 to print all terms*/, a=1, u=0, m=1, L=0)={for(i=2, n, verbose&&print1(a", "); u+=1<<a; while(bittest(u, m), m++); my(s=L+a); L=a; forprime(p=s+m, , bittest(u, p-s)&&next; a=p-s; break)); a}\\ could be made more efficient using Israel's comment and a second "m" for the (smallest possible) even terms. - M. F. Hasler, Dec 11 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Oct 25 2002
EXTENSIONS
More terms from David Garber, Oct 30 2002
STATUS
approved