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Primes of the form: nonprime(prime(n)) - (-1)^n.
0

%I #11 Oct 05 2024 14:35:09

%S 2,3,17,19,71,97,127,131,139,191,193,227,229,251,281,337,349,353,389,

%T 443,503,541,557,563,571,613,659,701,719,727,743,877,911,971,1031,

%U 1087,1091,1103,1217,1297,1301,1409,1439,1451,1481,1531,1549,1657,1697,1741

%N Primes of the form: nonprime(prime(n)) - (-1)^n.

%C Where n-th "prime nonprime" = A141468(A000040(n)) and 1st "prime nonprime" = 0.

%e For n=1, nonprime(prime(1)) - (-1)^1 = nonprime(2)+1 = 1+1 = 2 (prime), so a(1)=2.

%e For n=2, nonprime(prime(2)) - (-1)^2 = nonprime(3)-1 = 4-1 = 3(prime), so a(2)=3.

%e For n=3, nonprime(prime(3)) - (-1)^3 = nonprime(5)+1 = 8+1 = 9 (composite).

%e For n=4, nonprime(prime(4)) - (-1)^4 = nonprime(7)-1 = 10-1 = 9 (composite).

%e For n=5, nonprime(prime(5)) - (-1)^5 = nonprime(11)+1 = 16+1 = 17 (prime), so a(3)=17, etc.

%p A141468 := proc(n) if n <= 2 then n-1 ; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od; fi: end: for n from 1 to 400 do p := A141468(ithprime(n))-(-1)^n ; if isprime(p) then printf("%d,",p); fi; od: # _R. J. Mathar_, Aug 14 2009

%Y Cf. A000040, A141468.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 06 2009

%E Corrected and extended by _R. J. Mathar_, Aug 14 2009