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Primes of the form r(r(r(n)+1)+1)+1, where A141468(n)=r(n)=n-th nonprime.
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%I #5 Mar 30 2012 18:52:25

%S 2,17,23,31,37,47,67,71,97,101,103,109,127,131,137,139,149,151,157,

%T 163,179,191,197,199,211,223,227,233,239,241,257,263,269,271,277,281,

%U 283,311,313,331,347,349,353,359,367,373,379,389,397,401,419,431,443,449

%N Primes of the form r(r(r(n)+1)+1)+1, where A141468(n)=r(n)=n-th nonprime.

%e If n=1, then

%e r(r(r(1)+1)+1)+1=r(r(0+1)+1)+1=r(r(1)+1)+1=r(0+1)+1=r(1)+1=0+1=1

%e (nonprime).

%e If n=2, then

%e r(r(r(2)+1)+1)+1=r(r(1+1)+1)+1=r(r(2)+1)+1=r(1+1)+1=r(2)+1=1+1=2=a(1).

%e If n=3, then

%e r(r(r(3)+1)+1)+1=r(r(4+1)+1)+1=r(r(5)+1)+1=r(8+1)+1=r(9)+1=14+1=15

%e (nonprime).

%e If n=4, then

%e r(r(r(4)+1)+1)+1=r(r(6+1)+1)+1=r(r(7)+1)+1=r(10+1)+1=r(11)+1=16+1=17=a(2).

%e If n=5, then

%e r(r(r(5)+1)+1)+1=r(r(8+1)+1)+1=r(r(9)+1)+1=r(14+1)+1=r(15)+1=22+1=23=a(3).

%e If n=6, then

%e r(r(r(6)+1)+1)+1=r(r(9+1)+1)+1=r(r(10)+1)+1=r(15+1)+1=r(16)+1=24+1=25

%e (nonprime).

%e If n=7, then

%e r(r(r(7)+1)+1)+1=r(r(10+1)+1)+1=r(r(11)+1)+1=r(16+1)+1=r(17)+1=25+1=26

%e (nonprime).

%e If n=8, then

%e r(r(r(8)+1)+1)+1=r(r(12+1)+1)+1=r(r(13)+1)+1=r(20+1)+1=r(21)+1=30+1=31=a(4).

%e If n=9, then

%e r(r(r(9)+1)+1)+1=r(r(14+1)+1)+1=r(r(15)+1)+1=r(22+1)+1=r(23)+1=33+1=34

%e (nonprime).

%e If n=10, then

%e r(r(r(10)+1)+1)+1=r(r(15+1)+1)+1=r(r(16)+1)+1=r(24+1)+1=r(25)+1=35+1=36

%e (nonprime)

%e If n=11, then

%e r(r(r(11)+1)+1)+1=r(r(16+1)+1)+1=r(r(17)+1)+1=r(25+1)+1=r(26)+1=36+1=37=a(5),

%e etc.

%Y Cf. A000040, A141468.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Aug 25 2008

%E 67 inserted, 73 removed, 227 and 233 inserted and extended by _R. J. Mathar_, Sep 05 2008