OFFSET
1,1
COMMENTS
This asks for primes p which are a triangular number divided by 21, or, 2*3*7*p=k*(k+1) for some k. Matching factors shows that the sequence is complete [R. J. Mathar, Aug 15 2010]
Original definition: Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=21.
The corresponding m-values are m=14, 21, 41, 42 (cf. A154296). It is clear that for m>42, A000217(m)/21 = m(m+1)/42 cannot be a prime. - M. F. Hasler, Dec 31 2012
MATHEMATICA
lst={}; s=0; Do[s+=n/21; If[Floor[s]==s, If[PrimeQ[s], AppendTo[lst, s]]], {n, 0, 9!}]; lst
#/21&/@Select[Accumulate[Range[100]], PrimeQ[#/21]&] (* Harvey P. Dale, Dec 17 2012 *)
PROG
(PARI) select(x->denominator(x)==1 & isprime(x), vector(42, m, m^2+m)/42) \\ - M. F. Hasler, Dec 31 2012
CROSSREFS
KEYWORD
nonn,fini,full,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jan 06 2009
EXTENSIONS
Added keywords fini,full - R. J. Mathar, Aug 15 2010
Edited by M. F. Hasler, Dec 31 2012
STATUS
approved