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%I #25 Sep 01 2016 23:27:54
%S 13,31,47,67,79,89,97,103,113,149,173,179,211,223,241,277,313,349,359,
%T 379,449,457,487,503,509,631,743,769,797,809,887,937,967,1009,1049,
%U 1109,1123,1213,1231,1277,1289,1319,1409,1429,1453,1471,1489,1543,1571,1663
%N Primes of the form prime(k) + composite(k) for some k.
%C Conjecture: This sequence is infinite.
%H Robert Israel, <a href="/A111489/b111489.txt">Table of n, a(n) for n = 1..10000</a>
%e The third prime is 5, the third composite is 8, 8+5=13, the first entry.
%p Primes, Composites:= selectremove(isprime, [$2..10^4]):
%p select(isprime, Primes + Composites[1..nops(Primes)]); # _Robert Israel_, Jul 08 2016
%t nn = 222; Select[Total /@ Transpose@{#, Take[Complement[Range@ Prime@ nn, {1}~Join~#], nn]} &@ Prime@ Range@ nn, PrimeQ] (* _Michael De Vlieger_, Jul 08 2016 *)
%o (PARI) composite(n)= local(c, x); c=1; x=1; while(c <= n, x++; if(!isprime(x), c++); ); return(x);
%o g(n)=for(x=1,n,y=prime(x)+composite(x);if(isprime(y),print1(y",")))
%o (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
%Y Cf. A000040, A002808, A097452, A142348.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Nov 15 2005
%E Name corrected by _Adam Kubias_, Jul 08 2016
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