A111489 Primes of the form prime(k) + composite(k) for some k.

13, 31, 47, 67, 79, 89, 97, 103, 113, 149, 173, 179, 211, 223, 241, 277, 313, 349, 359, 379, 449, 457, 487, 503, 509, 631, 743, 769, 797, 809, 887, 937, 967, 1009, 1049, 1109, 1123, 1213, 1231, 1277, 1289, 1319, 1409, 1429, 1453, 1471, 1489, 1543, 1571, 1663

Offset

1,1

Comments

Conjecture: This sequence is infinite.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The third prime is 5, the third composite is 8, 8+5=13, the first entry.

Maple

Primes, Composites:= selectremove(isprime, [$2..10^4]):
select(isprime, Primes + Composites[1..nops(Primes)]); # Robert Israel, Jul 08 2016

Mathematica

nn = 222; Select[Total /@ Transpose@{#, Take[Complement[Range@ Prime@ nn, {1}~Join~#], nn]} &@ Prime@ Range@ nn, PrimeQ] (* Michael De Vlieger, Jul 08 2016 *)

Prog

(PARI) composite(n)= local(c, x); c=1; x=1; while(c <= n, x++; if(!isprime(x), c++); ); return(x);
g(n)=for(x=1, n, y=prime(x)+composite(x); if(isprime(y), print1(y", ")))
(PARI) list(lim)=my(v=List(), p=5, c=8, t); while((t=p+c) <= lim, if(isprime(t), listput(v, t)); p=nextprime(p+1); if(isprime(c++), c++)); Vec(v) \\ Charles R Greathouse IV, Sep 01 2016

Crossrefs

Cf. A000040, A002808, A097452, A142348.

Sequence in context: A080387 A348300 A100589 * A106294 A101649 A063305

Adjacent sequences: A111486 A111487 A111488 * A111490 A111491 A111492

Keyword

easy,nonn

Author

Cino Hilliard, Nov 15 2005

Extensions

Name corrected by Adam Kubias, Jul 08 2016

Status

approved