A154298 Primes of the form (1+...+m)/33 = A000217(m)/33, for some m.

2, 7, 17, 67

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Keywords

• nonn
• fini
• full
• easy

Comments

Primes which are some triangular number A000217 divided by 33. Finiteness is shown with the same strategy as in A154297.

Original definition: Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=33.

The corresponding m-values are m=11, 21, 33, 66 (cf. A154296). It is clear that for m>66, A000217(m)/33 = m(m+1)/66 cannot be a prime. - M. F. Hasler, Dec 31 2012

Crossrefs

Cf. A057570, A154293, A154296 - A154304.

Programs

Mathematica

lst={};s=0;Do[s+=n/33;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,9!}];lst
Select[Accumulate[Range[200]]/33,PrimeQ] (* Harvey P. Dale, Aug 11 2025 *)

PARI

select(x->denominator(x)==1 & isprime(x), vector(66, m, m^2+m)/66)  \\ - M. F. Hasler, Dec 31 2012

Extensions

Edited by M. F. Hasler, Dec 31 2012