This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A154298 #11 Aug 11 2025 10:16:01
%S A154298 2,7,17,67
%N A154298 Primes of the form (1+...+m)/33 = A000217(m)/33, for some m.
%C A154298 Primes which are some triangular number A000217 divided by 33. Finiteness is shown with the same strategy as in A154297.
%C A154298 Original definition: Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=33.
%C A154298 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 A154298 lst={};s=0;Do[s+=n/33;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,9!}];lst
%t A154298 Select[Accumulate[Range[200]]/33,PrimeQ] (* _Harvey P. Dale_, Aug 11 2025 *)
%o A154298 (PARI) select(x->denominator(x)==1 & isprime(x), vector(66, m, m^2+m)/66) \\ - _M. F. Hasler_, Dec 31 2012
%Y A154298 Cf. A057570, A154293, A154296 - A154304.
%K A154298 nonn,fini,full,easy
%O A154298 1,1
%A A154298 _Vladimir Joseph Stephan Orlovsky_, Jan 06 2009
%E A154298 Edited by _M. F. Hasler_, Dec 31 2012