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%I #11 Jun 24 2015 14:41:45
%S 3,13,29,113
%N Primes of the form (1+2+...+m)/57 = A000217(m)/57.
%C Original definition: "Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=57."
%C Primes which are some triangular number divided by 57. Finiteness of the sequence follows along the reasoning in A154297.
%C 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 lst={};s=0;Do[s+=n/57;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,2*9!}];lst
%t Select[Accumulate[Range[1000]]/57,PrimeQ] (* _Harvey P. Dale_, Jun 24 2015 *)
%o (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 Cf. A057570, A154293, A154296 - A154304.
%K nonn,fini,full
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 06 2009
%E Keywords fini,full added by _R. J. Mathar_, Aug 15 2010
%E Edited by _M. F. Hasler_, Jan 06 2013
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