A154303 - OEIS

%I #8 Jan 06 2013 17:22:49

%S 7,11,179,181

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

%C Original definition: "Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=90."

%C 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

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

%o (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

%Y Cf. A057570, A154293, A154296 - A154304.

%K nonn,fini,full,easy,bref

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 06 2009

%E Edited by _M. F. Hasler_, Jan 06 2013