|
%I #10 Sep 03 2023 06:05:15
%S 3,17,47,419,421
%N Primes of the form (1+2+...+m)/210 = A000217(m)/210.
%C Original definition : Primes of the form 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=210.
%C 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
%t lst={};s=0;Do[s+=n/210;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,6*9!}];lst
%o (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
%Y Cf. A057570, A154293, A154296 - A154303.
%K nonn,fini,full
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 06 2009
%E Edited by _M. F. Hasler_, Jan 06 2013
|
