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 A154299 #18 Jun 25 2021 23:14:08
%S A154299 3,11,101,103
%N A154299 Primes of the form (1+...+m)/51 = A000217(m)/51.
%C A154299 Primes p of the form k*(k+1)/(2*51): There is a finite set of solutions to 2*3*17*p=k*(k+1). - _R. J. Mathar_, Aug 15 2010
%C A154299 Original definition: "Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=51."
%C A154299 The corresponding m-values are m=17, 33, 101, 102 (cf. A154296-A154304, see the latter for more comments and PARI code). It is clear that for m>102, A000217(m)/51 = m(m+1)/102 has at least 2 factors and hence cannot be prime. - _M. F. Hasler_, Dec 31 2012
%t A154299 lst={};s=0;Do[s+=n/51;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,9!}];lst
%t A154299 Select[Accumulate[Range[1000]/51],PrimeQ] (* _Harvey P. Dale_, Jun 21 2012 *)
%o A154299 (PARI) M=51*2;select(x->denominator(x)==1 & isprime(x), vector(M, m, m^2+m)/M) \\ _M. F. Hasler_, Dec 31 2012
%Y A154299 Cf. A057570, A154293, A154296 - A154304.
%K A154299 nonn,fini,full,easy
%O A154299 1,1
%A A154299 _Vladimir Joseph Stephan Orlovsky_, Jan 06 2009
%E A154299 Keywords fini,full added by _R. J. Mathar_, Aug 15 2010