%I #14 Feb 05 2014 10:58:29

%S 3,3,5,11,11,11,13,17,17,19,23,23,29,29,29,31,37,37,37,41,41,43,47,47,

%T 53,53,53,59,59,59,61,67,67,67,71,71,73,79,79,79,83,83,89,89,89,19,29,

%U 29,31,47,47,67,71,71,73,89,89,103,107,107,109,113,113

%N Define a(4)=3, then a(n+1) is the smallest prime P such that a(n) <= P < 2*n with 2*n-P=Q prime and, if not possible, a(n+1) is the smallest prime P such that P < a(n) < 2*n with 2*n-P=Q prime.

%H Pierre CAMI, <a href="/A235859/b235859.txt">Table of n, a(n) for n = 4..10005</a>

%e a(4)=3 as 2*4-3=5 prime by definition

%e a(5)=3 as 2*5-3=7 prime, a(5)=a(4), a(5)<5

%e a(6)=5 as 2*6-5=7 prime, a(6)>a(5), a(6)<6

%e a(7)=5 not possible as 14-5=9 composite

%e a(7)=7 not possible as 7=7

%e a(7)=11 as 2*7-11=3 prime

%e .........................

%e a(48)=89 as 2*48-89=7 prime

%e a(49)=89 not possible as 2*49-89=9 composite

%e a(49)=97 not possible as 2*49-97=unity

%e a(49)=19 as 19 is the smallest prime such that 2*49-19 is prime

%e a(50)=29 as 29 is the smallest prime >=19 such that 2*50-29 is prime

%o (PFGW & SCRIPT)

%o SCRIPT

%o DIM n,3

%o DIM i

%o DIM pp

%o DIMS t

%o OPENFILEOUT myf,a(n).txt

%o LABEL loop1

%o OPENFILEIN maf,prime.txt

%o GETNEXT i,maf

%o GETNEXT i,maf

%o LABEL a

%o SET n,n+1

%o IF n>10005 THEN END

%o SET pp,2*n-i

%o SETS t,%d,%d\,;n;i

%o PRP pp,t

%o IF ISPRP THEN GOTO c

%o LABEL b

%o GETNEXT i,maf

%o IF i==n THEN GOTO b

%o IF 2*n-i<3 THEN GOTO d

%o SET pp,2*n-i

%o SETS t,%d,%d\,;n;i

%o PRP pp,t

%o IF ISPRP THEN GOTO c

%o GOTO b

%o LABEL c

%o WRITE myf,t

%o GOTO a

%o LABEL d

%o CLOSEFILE maf

%o SET n,n-1

%o GOTO loop1

%Y Cf. A002373, A020483, A235649.

%K nonn,less

%O 4,1

%A _Pierre CAMI_, Jan 16 2014