A154301 Primes of the form (1+2+...+m)/75 = A000217(m)/75.

17, 37, 149, 151

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Keywords

• nonn
• fini
• full
• easy
• bref

Comments

Original definition: "Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=75."

The corresponding m-values are m=50,74,149,150. It is clear that for m>2*75, T(m)/75 = m(m+1)/150 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/75;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,3*9!}];lst

PARI

d=75*2;for(m=1,999,(m^2+m)%d==0&isprime((m^2+m)/d)&print1(m",")) \\ print the m-values(!) - use A154304(75) to get A154301 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