login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A100718 Composite numbers C(p) such that p and C(p)-p are primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 16:46 EDT 2019. Contains 328373 sequences. (Running on oeis4.)