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A141557 Nonprimes of form (p(c(n))-c(p(n))), where c(n)=n-th composite and p(n)=n-th prime. 0

%I #3 Mar 30 2012 18:52:27

%S 1,9,9,9,15,16,18,25,21,27,26,21,22,21,35,38,35,34,33,39,49,49,33,52,

%T 49,39,48,48,49,48,60,49,52,58,58,63,75,65,65,75,81,84,77,65,69,72,72,

%U 69,65,65,75,68,77,86,94,85,95,90,94,88,98,102,99,96,93,94,94,100,91,87,90

%N Nonprimes of form (p(c(n))-c(p(n))), where c(n)=n-th composite and p(n)=n-th prime.

%e If n=1, c(1)=4, p(1)=2, then p(4)-c(2)=7-6=1=a(1).

%e If n=2, c(2)=6, p(2)=3, then p(6)-c(3)=13-8=5 (prime).

%e If n=3, c(3)=8, p(3)=5, then p(8)-c(5)=19-10=9=a(2).

%e If n=4, c(4)=9, p(4)=7, then p(9)-c(7)=23-14=9=a(3).

%e If n=5, c(5)=10, p(5)=11, then p(10)-c(11)=29-20=9=a(4).

%e If n=6, c(6)=12, p(6)=13, then p(12)-c(13)=37-22=15=a(5).

%e If n=7, c(7)=14, p(7)=17, then p(14)-c(17)=43-27=16=a(6).

%e If n=8, c(8)=15, p(8)=19, then p(15)-c(19)=47-30=17 (prime).

%e If n=9, c(9)=16, p(9)=23, then p(16)-c(23)=53-35=18=a(7).

%e If n=10, c(10)=18, p(10)=29, then=p(18)-c(29)=61-44=17 (prime).

%e If n=11, c(11)=20, p(11)=31, then p(20)-c(31)=71-46=25=a(8).

%e If n=12, c(12)=21, p(12)=37, then p(21)-c(37)=73-54=19 (prime).

%e If n=13, c(13)=22, p(13)=41, then p(22)-c(41)=79-58=21=a(9).

%e If n=14, c(14)=24, p(14)=43, then p(24)-c(43)=89-62=27=a(10).

%e If n=15, c(15)=25, p(15)=47, then p(25)-c(47)=97-66=31 (prime).

%e If n=16, c(16)=26, p(16)=53, then p(26)-c(53)=101-75=26=a(11), etc.

%Y Cf. A000040, A002808.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Aug 14 2008

%E Edited, corrected and extended by _Ray Chandler_, Aug 19 2008

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