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A217696 Let p = A002145(n) be the n-th 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)+2-p 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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified January 18 13:44 EST 2020. Contains 331008 sequences. (Running on oeis4.)