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

7, 11, 179, 181

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=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

Crossrefs

Cf. A057570, A154293, A154296 - A154304.

Programs

Mathematica

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

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

Extensions

Edited by M. F. Hasler, Jan 06 2013