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 A154296 #22 Jul 22 2023 14:13:57
%S A154296 3,7,29,31
%N A154296 Primes of the form (1+2+3+...+m)/15 = A000217(m)/15, for some m.
%C A154296 Original definition: Primes of the form 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=15.
%C A154296 The corresponding m-values are m=9, 14, 29, 30. It is clear that for m > 30, T(m)/15 = m*(m+1)/30 cannot be a prime. - _M. F. Hasler_, Dec 31 2012
%C A154296 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
%C A154296 Also primes p such that 120*p+1 is a perfect square. - _Lamine Ngom_, Jul 22 2023
%t A154296 lst={};s=0;Do[s+=n/15;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,9!}];lst
%t A154296 Select[(Accumulate[Range[200]])/15,PrimeQ] (* _Harvey P. Dale_, Oct 30 2011 *)
%o A154296 (PARI) select(x->denominator(x)==1 & isprime(x), vector(30,m,m^2+m)/30) \\ _M. F. Hasler_, Dec 31 2012
%Y A154296 Cf. A057570, A154293, A154297, A154298, A154299, A154300, A154301, A154302, A154303, A154304.
%K A154296 nonn,fini,full,easy
%O A154296 1,1
%A A154296 _Vladimir Joseph Stephan Orlovsky_, Jan 06 2009
%E A154296 Edited by _M. F. Hasler_, Dec 31 2012