|
%I #15 Jan 29 2023 09:16:56
%S 13,29,37,59,127,137,151,163,227,263,271,337,467,563,683,701,727,809,
%T 941,967,1069,1187,1213,1279,1607,1867,1901,1913,1993,2099,2137,2473,
%U 2791,2819,2927,3049,3359,3571,3761,3823,4027,4093,4297,4643,4721,4831
%N Primes of the form c(p(n)) + p(c(n)), where c(n) = n-th composite and p(n) = n-th prime.
%e For n= 1, c(1) = 4, p(1) = 2; c(2) + p(4) = 6+ 7= 13 = a(1).
%e For n= 2, c(2) = 6, p(2) = 3; c(3) + p(6) = 8+13= 21 (nonprime).
%e For n= 3, c(3) = 8, p(3) = 5; c(5) + p(8) = 10+19= 29 = a(2).
%e For n= 4, c(4) = 9, p(4) = 7; c(7) + p(9) = 14+23= 37 = a(3).
%e For n= 5, c(5) =10, p(5) =11; c(11) + p(10) = 20+29= 49 (nonprime).
%e For n= 6, c(6) =12, p(6) =13; c(13) + p(12) = 22+37= 59 = a(4).
%o (PARI) p(n) = prime(n); \\ A000040
%o c(n) = for(k=0, primepi(n), isprime(n++)&&k--); n; \\ A002808
%o select(isprime, vector(70, n, c(p(n)) + p(c(n)))) \\ _Michel Marcus_, Jan 29 2023
%Y Cf. A000040, A002808, A141554.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Aug 14 2008
%E Edited and extended by _Ray Chandler_, Aug 19 2008
|
