A154300 Primes of the form (1+2+...+m)/57 = A000217(m)/57.

3, 13, 29, 113

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Keywords

• nonn
• fini
• full

Comments

Original definition: "Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=57."

Primes which are some triangular number divided by 57. Finiteness of the sequence follows along the reasoning in A154297.

The corresponding m-values are m=18,38,57,113. It is clear that for m>2*57, T(m)/57 = m(m+1)/114 cannot be a prime, since then each factor in the numerator is larger than the denominator. See A154304 for further comments and PARI code. - M. F. Hasler, Jan 06 2013

Crossrefs

Cf. A057570, A154293, A154296 - A154304.

Programs

Mathematica

lst={};s=0;Do[s+=n/57;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,2*9!}];lst
Select[Accumulate[Range[1000]]/57,PrimeQ] (* Harvey P. Dale, Jun 24 2015 *)

PARI

d=57*2;for(m=1,999,(m^2+m)%d==0&isprime((m^2+m)/d)&print1(m",")) \\ print the m-values(!) - use A154304(57) to get A154300 as a vector. \\ - M. F. Hasler, Jan 06 2013

Extensions

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

Edited by M. F. Hasler, Jan 06 2013