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A154300
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Primes of the form (1+2+...+m)/57 = A000217(m)/57.
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3
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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