A097452 Primes of the form prime(k) + nonprime(k) for some k.

3, 7, 11, 23, 29, 71, 101, 139, 151, 157, 199, 229, 239, 251, 263, 311, 347, 367, 401, 443, 479, 547, 601, 653, 673, 691, 709, 853, 977, 991, 1013, 1051, 1087, 1181, 1237, 1291, 1327, 1451, 1487, 1579, 1637, 1693, 1721, 1753, 1777, 1861, 1877, 1913, 1951

Offset

1,1

Comments

Are there infinitely many such primes?

Links

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

Example

The 6th prime is 13, the 6th nonprime is 10, 13 + 10 = 23 so 23 is in this sequence.

Maple

Primes, Nonprimes:= selectremove(isprime, [$1..10^5]):
select(isprime, Primes + Nonprimes[1..nops(Primes)]); # Robert Israel, Jul 08 2016

Mathematica

primepcomp[n_] := Reap[For[x = 1, x <= n, x++, y = Prime[x] + composite[x]; If[PrimeQ[y], Sow[y]]]][[2, 1]]; composite[n_] := Module[{c = 1, x = 0}, While[c <= n, x++; If[!PrimeQ[x], c++]]; x]; primepcomp[300] (* Jean-François Alcover, Nov 18 2013, translated from Pari *)
nn = 262; Select[Total /@ Transpose@ {#, Take[Complement[Range@ Prime@ nn, #], nn]} &@ Prime@ Range@ nn, PrimeQ] (* Michael De Vlieger, Jul 08 2016 *)

Prog

(PARI) composite(n)= local(c, x); c=1; x=0; while(c <= n, x++; if(!isprime(x), c++); ); x
primepcomp(n) = for(x=1, n, y=prime(x)+ composite(x); if(isprime(y), print1(y", ")))
(PARI) list(lim)=my(v=List([3]), n=4, p=3, t); while((t=n+p)<=lim, if(isprime(t), listput(v, t)); p=nextprime(p+1); if(isprime(n++), n++)); Vec(v) \\ Charles R Greathouse IV, Sep 01 2016

Crossrefs

Cf. A000040, A018252, A111489, A142348.

Sequence in context: A187106 A111668 A112038 * A086505 A239227 A154427

Adjacent sequences: A097449 A097450 A097451 * A097453 A097454 A097455

Keyword

easy,nonn

Author

Cino Hilliard, Aug 23 2004

Extensions

Name corrected by Adam Kubias, Jul 08 2016

Status

approved