

A217696


Let p = A002145(n) be the nth prime of the form 4k+3, then a(n) is the smallest number such that p is the smallest prime of the form 4k+3 for which 4*a(n)+2p is prime.


3



1, 4, 10, 24, 76, 102, 196, 74, 104, 348, 314, 345, 86, 660, 443, 1494, 914, 1329, 2613, 1635, 1316, 1856, 1688, 2589, 2628, 6423, 3116, 2165, 6320, 4445, 7278, 4743, 16539, 17783, 6084, 3806, 6281, 8946, 15129, 6266, 10976, 19538, 16794, 31160, 32916, 57041
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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 nth 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(np), return(0)); forprime(q=2, p1, if(q%4==3 && isprime(nq), 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

Cf. A214834, A016825, A000040, A002145, A155642.
Sequence in context: A212330 A291412 A001868 * A223014 A038783 A127070
Adjacent sequences: A217693 A217694 A217695 * A217697 A217698 A217699


KEYWORD

nonn


AUTHOR

Lei Zhou, Mar 19 2013


STATUS

approved



