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%I #9 Jan 06 2013 16:01:41
%S 2,7,17,67
%N Primes of the form (1+...+m)/33 = A000217(m)/33, for some m.
%C Primes which are some triangular number A000217 divided by 33. Finiteness is shown with the same strategy as in A154297.
%C Original definition: Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=33.
%C The corresponding m-values are m=11, 21, 33, 66 (cf. A154296). It is clear that for m>66, A000217(m)/33 = m(m+1)/66 cannot be a prime. - _M. F. Hasler_, Dec 31 2012
%t lst={};s=0;Do[s+=n/33;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,9!}];lst
%o (PARI) select(x->denominator(x)==1 & isprime(x), vector(66, m, m^2+m)/66) \\ - _M. F. Hasler_, Dec 31 2012
%Y Cf. A057570, A154293, A154296 - A154304.
%K nonn,fini,full,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 06 2009
%E Edited by _M. F. Hasler_, Dec 31 2012
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