

A154297


Primes of the form (1+2+3+...+m)/21 = A000217(m)/21, for some m.


3




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 mvalues 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


LINKS

Table of n, a(n) for n=1..4.


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

Cf. A057570, A154293, A154296, A154298, A154299, A154300, A154301, A154302, A154303, A154304.
Sequence in context: A276663 A187984 A063626 * A089441 A046121 A023271
Adjacent sequences: A154294 A154295 A154296 * A154298 A154299 A154300


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



