A154299 Primes of the form (1+...+m)/51 = A000217(m)/51.

3, 11, 101, 103

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Keywords

• nonn
• fini
• full
• easy

Comments

Primes p of the form k*(k+1)/(2*51): There is a finite set of solutions to 2*3*17*p=k*(k+1). - 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=51."

The corresponding m-values are m=17, 33, 101, 102 (cf. A154296-A154304, see the latter for more comments and PARI code). It is clear that for m>102, A000217(m)/51 = m(m+1)/102 has at least 2 factors and hence cannot be prime. - M. F. Hasler, Dec 31 2012

Crossrefs

Cf. A057570, A154293, A154296 - A154304.

Programs

Mathematica

lst={};s=0;Do[s+=n/51;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,9!}];lst
Select[Accumulate[Range[1000]/51],PrimeQ] (* Harvey P. Dale, Jun 21 2012 *)

PARI

M=51*2;select(x->denominator(x)==1 & isprime(x), vector(M, m, m^2+m)/M)  \\ M. F. Hasler, Dec 31 2012

Extensions

Keywords fini,full added by R. J. Mathar, Aug 15 2010