A100718 Composite numbers C(p) such that p and C(p)-p are primes.

8, 10, 14, 30, 54, 58, 62, 66, 82, 108, 114, 120, 178, 182, 204, 210, 318, 324, 330, 352, 366, 430, 506, 544, 560, 586, 596, 616, 704, 738, 792, 858, 870, 914, 918, 960, 988, 990, 1026, 1030, 1062, 1164, 1170, 1194, 1404, 1442, 1446, 1462, 1464, 1470, 1498

Offset

1,1

Comments

Nextprime(C(n)) = P(C(n) - n) = (C(n) - n)-th prime.

A proof that the sequence is infinite would be nice.

Links

Table of n, a(n) for n=1..51.

Formula

C(n)=n+k where k is such that nextprime(C(n))=k-th prime.

Example

a(4)=30 because C(19)=30=19+11, 19 and 11 are prime and P(11)=31=nextprime(30).

Mathematica

Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n]; Composite /@ Select[ Prime[ Range[ 205]], PrimeQ[ Composite[ # ] - # ] &] (* Robert G. Wilson v, Dec 11 2004 *)
Reap[For[n = 4; p = 1, n <= 1500, n++, If[! PrimeQ[n], If[PrimeQ[p] && PrimeQ[n-p], Sow[n]]; p++]]] [[2, 1]]  (* Jean-François Alcover, Jul 18 2013 *)

Crossrefs

Sequence in context: A196226 A250290 A228946 * A063190 A101763 A154568

Adjacent sequences: A100715 A100716 A100717 * A100719 A100720 A100721

Keyword

nonn

Author

Robin Garcia, Dec 11 2004

Extensions

Edited and extended by Robert G. Wilson v, Dec 11 2004

Status

approved