A106736 Primes of the form r(r(r(r(n)+1)+1)+1)+1, where A141468(n) = r(n) = n-th nonprime.

2, 23, 37, 67, 71, 101, 103, 109, 127, 137, 139, 151, 157, 179, 191, 197, 199, 211, 227, 233, 239, 241, 257, 263, 271, 277, 281, 283, 311, 331, 347, 353, 359, 367, 373, 379, 389, 401, 419, 431, 443, 457, 461, 467, 499, 503, 509, 521, 523, 541, 547, 557, 563

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 25 2008

Keywords

• nonn

Examples

			n=1:
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
(nonprime).
n=2:
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).
n=3:
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).
n=4:
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
(nonprime).
n=5:
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
(nonprime).
n=6:
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
35+1=36 (nonprime).
n=7:
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
36+1=37=a(3).
n=8:
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
(nonprime).
n=9:
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
48+1=49 (nonprime).
n=10:
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
50+1=51(nonprime)
n=11:
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),
etc.
		

Crossrefs

Cf. A000040, A141468.

Programs

Maple

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: # R. J. Mathar, Sep 05 2008

Extensions

97 removed and extended by R. J. Mathar, Sep 05 2008