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

3, 17, 47, 419, 421

Offset

1,1

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

Links

Table of n, a(n) for n=1..5.

Mathematica

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

Prog

(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

Crossrefs

Cf. A057570, A154293, A154296 - A154303.

Sequence in context: A117012 A162291 A095697 * A144640 A084069 A297514

Adjacent sequences: A154301 A154302 A154303 * A154305 A154306 A154307

Keyword

nonn,fini,full

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Extensions

Edited by M. F. Hasler, Jan 06 2013

Status

approved