A154303 Primes of the form (1+2+...+m)/90 = A000217(m)/90.

7, 11, 179, 181

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=90."

The corresponding m-values are m=35,44,179,180. It is clear that for m>180, T(m)/90 = m(m+1)/180 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..4.

Mathematica

lst={}; s=0; Do[s+=n/90; If[Floor[s]==s, If[PrimeQ[s], AppendTo[lst, s]]], {n, 0, 5*9!}]; lst

Prog

(PARI) d=90*2; for(m=1, 999, (m^2+m)%d==0&isprime((m^2+m)/d)&print1(m", ")) \\ print the m-values(!) - use A154304(90) to get A154303 as a list/vector. \\ - M. F. Hasler, Jan 06 2013

Crossrefs

Cf. A057570, A154293, A154296 - A154304.

Sequence in context: A335813 A038543 A145953 * A128340 A106716 A292791

Adjacent sequences: A154300 A154301 A154302 * A154304 A154305 A154306

Keyword

nonn,fini,full,easy,bref

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Extensions

Edited by M. F. Hasler, Jan 06 2013

Status

approved