OFFSET
1,2
COMMENTS
It is conjectured that a(n) is defined for all positive integers.
This is also the index of first occurrence of the n-th prime in the form of 4k+3 in A214834.
LINKS
Lei Zhou, Table of n, a(n) for n = 1..170
EXAMPLE
n=1: the first prime in the form of 4k+3 is 3, 3+3=6=4*1+2, so a(1)=1;
n=2: the second prime in the form of 4k+3 is 7, 7+7=14=3+11=4*3+2, and 11 is also a prime in the form of 4k+3, so a(2)!=3. 7+11=18=4*4+2=3+15, and 15 is not a prime number. So a(2)=4.
MATHEMATICA
goal = 46; plst = {}; pct = 0; clst = {}; n = -1; While[pct < goal,
n = n + 4; If[PrimeQ[n], AppendTo[plst, n]; AppendTo[clst, 0];
pct++]]; n = 2; cct = 0; While[cct < goal, n = n + 4; p1 = n + 1;
While[p1 = p1 - 4; p2 = n - p1; ! ((PrimeQ[p1]) && (PrimeQ[p2]) && (Mod[p2, 4] == 3))]; If[MemberQ[plst, p2], If[id = Position[plst, p2][[1, 1]]; clst[[id]] == 0, clst[[id]] = (n - 2)/4; cct++]]]; clst
PROG
(PARI) ok(n, p)=if(!isprime(n-p), return(0)); forprime(q=2, p-1, if(q%4==3 && isprime(n-q), return(0))); 1
a(n)=my(p, k); forprime(q=2, , if(q%4==3&&n--==0, p=q; break)); k=(p+1)/4; while(!ok(4*k+2, p), k++); k \\ Charles R Greathouse IV, Mar 19 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Lei Zhou, Mar 19 2013
STATUS
approved