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A097452 Primes of the form prime(k) + nonprime(k) for some k. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified September 21 00:17 EDT 2019. Contains 327252 sequences. (Running on oeis4.)