A154304 Primes of the form (1+2+...+m)/210 = A000217(m)/210.

3, 17, 47, 419, 421

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=210.

The corresponding m-values are m=35,84,140,419,420. It is clear that for m>420, T(m)/210 = m(m+1)/420 cannot be a prime, since then each factor in the numerator is larger than the denominator. All of the sequences A154296, ..., A154304 could or should be grouped together in a single ("fuzzy"?) table. It would be more interesting to have the function f(n) which gives the *number* of primes of the form T(k)/n. - M. F. Hasler, Jan 06 2013

Crossrefs

Cf. A057570, A154293, A154296 - A154303.

Programs

Mathematica

lst={};s=0;Do[s+=n/210;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,6*9!}];lst

PARI

A154304(d=210)={select(x->denominator(x)==1 && isprime(x), vector(d*=2, m, m^2+m)/d)}  \\ - M. F. Hasler, Jan 06 2013

Extensions

Edited by M. F. Hasler, Jan 06 2013