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 A154300 #11 Jun 24 2015 14:41:45
%S A154300 3,13,29,113
%N A154300 Primes of the form (1+2+...+m)/57 = A000217(m)/57.
%C A154300 Original definition: "Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=57."
%C A154300 Primes which are some triangular number divided by 57. Finiteness of the sequence follows along the reasoning in A154297.
%C A154300 The corresponding m-values are m=18,38,57,113. It is clear that for m>2*57, T(m)/57 = m(m+1)/114 cannot be a prime, since then each factor in the numerator is larger than the denominator. See A154304 for further comments and PARI code. - _M. F. Hasler_, Jan 06 2013
%t A154300 lst={};s=0;Do[s+=n/57;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,2*9!}];lst
%t A154300 Select[Accumulate[Range[1000]]/57,PrimeQ] (* _Harvey P. Dale_, Jun 24 2015 *)
%o A154300 (PARI) d=57*2;for(m=1,999,(m^2+m)%d==0&isprime((m^2+m)/d)&print1(m",")) \\ print the m-values(!) - use A154304(57) to get A154300 as a vector. \\ - _M. F. Hasler_, Jan 06 2013
%Y A154300 Cf. A057570, A154293, A154296 - A154304.
%K A154300 nonn,fini,full
%O A154300 1,1
%A A154300 _Vladimir Joseph Stephan Orlovsky_, Jan 06 2009
%E A154300 Keywords fini,full added by _R. J. Mathar_, Aug 15 2010
%E A154300 Edited by _M. F. Hasler_, Jan 06 2013