A154297 Primes of the form (1+2+3+...+m)/21 = A000217(m)/21, for some m.

5, 11, 41, 43

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Keywords

• nonn
• fini
• full
• easy

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

Crossrefs

Cf. A057570, A154293, A154296, A154298, A154299, A154300, A154301, A154302, A154303, A154304.

Programs

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 *)

PARI

select(x->denominator(x)==1 & isprime(x), vector(42, m, m^2+m)/42)  \\ - M. F. Hasler, Dec 31 2012

Extensions

Added keywords fini,full - R. J. Mathar, Aug 15 2010

Edited by M. F. Hasler, Dec 31 2012