A154300 Primes of the form (1+2+...+m)/57 = A000217(m)/57.

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

Links

Table of n, a(n) for n=1..4.

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

Cf. A057570, A154293, A154296 - A154304.

Sequence in context: A023553 A268184 A183436 * A051805 A352267 A330451

Adjacent sequences: A154297 A154298 A154299 * A154301 A154302 A154303

Keyword

nonn,fini,full

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Extensions

Keywords fini,full added by R. J. Mathar, Aug 15 2010

Edited by M. F. Hasler, Jan 06 2013

Status

approved