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A154300
Primes of the form (1+2+...+m)/57 = A000217(m)/57.
3
3, 13, 29, 113
OFFSET
1,1
COMMENTS
Original definition: "Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=57."
Primes which are some triangular number divided by 57. Finiteness of the sequence follows along the reasoning in A154297.
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
MATHEMATICA
lst={}; s=0; Do[s+=n/57; If[Floor[s]==s, If[PrimeQ[s], AppendTo[lst, s]]], {n, 0, 2*9!}]; lst
Select[Accumulate[Range[1000]]/57, PrimeQ] (* Harvey P. Dale, Jun 24 2015 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
EXTENSIONS
Keywords fini,full added by R. J. Mathar, Aug 15 2010
Edited by M. F. Hasler, Jan 06 2013
STATUS
approved