Search: id:A106736
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%I A106736
%S A106736 2,23,37,67,71,101,103,109,127,137,139,151,157,179,191,197,199,211,227,
%T A106736 233,239,241,257,263,271,277,281,283,311,331,347,353,359,367,373,379,
%U A106736 389,401,419,431,443,457,461,467,499,503,509,521,523,541,547,557,563
%N A106736 Primes of the form r(r(r(r(n)+1)+1)+1)+1, where A141468(n)=r(n)=n-th 
               nonprime.
%e A106736 If n=1, then
%e A106736 r(r(r(r(1)+1)+1)+1)+1=r(r(r(0+1)+1)+1)+1=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 A106736 (nonprime).
%e A106736 If n=2, then
%e A106736 r(r(r(r(2)+1)+1)+1)+1=r(r(r(1+1)+1)+1)+1=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 A106736 If n=3, then
%e A106736 r(r(r(r(3)+1)+1)+1)+1=r(r(r(4+1)+1)+1)+1=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(2).
%e A106736 If n=4, then
%e A106736 r(r(r(r(4)+1)+1)+1)+1=r(r(r(6+1)+1)+1)+1=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 A106736 (nonprime).
%e A106736 If n=5, then
%e A106736 r(r(r(r(5)+1)+1)+1)+1=r(r(r(8+1)+1)+1)+1=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 A106736 (nonprime).
%e A106736 If n=6, then
%e A106736 r(r(r(r(6)+1)+1)+1)+1=r(r(r(9+1)+1)+1)+1=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
%e A106736 35+1=36 (nonprime).
%e A106736 If n=7, then
%e A106736 r(r(r(r(7)+1)+1)+1)+1=r(r(r(10+1)+1)+1)+1=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
%e A106736 36+1=37=a(3).
%e A106736 If n=8, then
%e A106736 r(r(r(r(8)+1)+1)+1)+1=r(r(r(12+1)+1)+1)+1=r(r(r(13)+1)+1)+1=r(r(20+1)+1)+1=r(r(21)+1)+1=r(30+1)+1=r(31)+1=44+\
               1=45
%e A106736 (nonprime).
%e A106736 If n=9, then
%e A106736 r(r(r(r(9)+1)+1)+1)+1=r(r(r(14+1)+1)+1)+1=r(r(r(15)+1)+1)+1=r(r(22+1)+1)+1=r(r(23)+1)+1=r(33+1)+1=r(34)+1
%e A106736 48+1=49 (nonprime).
%e A106736 If n=10, then
%e A106736 r(r(r(r(10)+1)+1)+1)+1=r(r(r(15+1)+1)+1)+1=r(r(r(16)+1)+1)+1=r(r(24+1)+1)+1=r(r(25)+1)+1=r(35+1)+1=r(36)+1
%e A106736 50+1=51(nonprime)
%e A106736 If n=11, then
%e A106736 r(r(r(r(11)+1)+1)+1)+1=r(r(r(16+1)+1)+1)+1=r(r(r(17)+1)+1)+1=r(r(25+1)+1)+1=r(r(26)+1)+1=r(36+1)+1=r(37)+1=51\
               +1=52(nonprime),
%e A106736 etc.
%p A106736 A141468 := proc(n) option remember ; if n = 1 then 0; else for a from 
               procname(n-1)+1 do if not isprime(a) then RETURN(a); fi; od: fi; 
               end: rep := 4: for n from 1 to 400 do arep := n ; for i from 1 to 
               rep do arep := A141468(arep)+1 ; od: if isprime(arep) then printf("%d,
               ",arep) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Sep 05 2008]
%Y A106736 Cf. A000040, A141468.
%Y A106736 Sequence in context: A007510 A117242 A144550 this_sequence A045392 A107374 
               A068835
%Y A106736 Adjacent sequences: A106733 A106734 A106735 this_sequence A106737 A106738 
               A106739
%K A106736 nonn
%O A106736 1,1
%A A106736 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Aug 25 2008
%E A106736 97 removed and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Sep 05 2008

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