A141555 Primes of the form c(p(n)) + p(c(n)), where c(n) = n-th composite and p(n) = n-th prime.

13, 29, 37, 59, 127, 137, 151, 163, 227, 263, 271, 337, 467, 563, 683, 701, 727, 809, 941, 967, 1069, 1187, 1213, 1279, 1607, 1867, 1901, 1913, 1993, 2099, 2137, 2473, 2791, 2819, 2927, 3049, 3359, 3571, 3761, 3823, 4027, 4093, 4297, 4643, 4721, 4831

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 14 2008

Keywords

• nonn

Examples

			For n= 1, c(1) = 4, p(1) = 2; c(2)  + p(4)  =  6+ 7=  13 = a(1).
For n= 2, c(2) = 6, p(2) = 3; c(3)  + p(6)  =  8+13=  21 (nonprime).
For n= 3, c(3) = 8, p(3) = 5; c(5)  + p(8)  = 10+19=  29 = a(2).
For n= 4, c(4) = 9, p(4) = 7; c(7)  + p(9)  = 14+23=  37 = a(3).
For n= 5, c(5) =10, p(5) =11; c(11) + p(10) = 20+29=  49 (nonprime).
For n= 6, c(6) =12, p(6) =13; c(13) + p(12) = 22+37=  59 = a(4).
		

Crossrefs

Cf. A000040, A002808, A141554.

Programs

PARI

p(n) = prime(n); \\ A000040
c(n) = for(k=0, primepi(n), isprime(n++)&&k--); n; \\ A002808
select(isprime, vector(70, n, c(p(n)) + p(c(n)))) \\ Michel Marcus, Jan 29 2023

Extensions

Edited and extended by Ray Chandler, Aug 19 2008