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 A111489 Primes of the form prime(k) + composite(k) for some k. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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: A129864 A080387 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

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)