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%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
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