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

3, 11, 101, 103

Offset

1,1

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

Links

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

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 *)

Prog

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

Crossrefs

Cf. A057570, A154293, A154296 - A154304.

Sequence in context: A008561 A348154 A072640 * A007616 A121045 A092245

Adjacent sequences: A154296 A154297 A154298 * A154300 A154301 A154302

Keyword

nonn,fini,full,easy

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Extensions

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

Status

approved