A154296 Primes of the form (1+2+3+...+m)/15 = A000217(m)/15, for some m.

3, 7, 29, 31

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Keywords

• nonn
• fini
• full
• easy

Comments

Original definition: Primes of the form 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=15.

The corresponding m-values are m=9, 14, 29, 30. It is clear that for m > 30, T(m)/15 = m*(m+1)/30 cannot be a prime. - M. F. Hasler, Dec 31 2012

All of the sequences A154296, ..., A154304 could or should be grouped together in a single ("fuzzy"?) table. It would be more interesting to have the function f(n) which gives the *number* of primes of the form T(k)/n. - M. F. Hasler, Jan 06 2013

Also primes p such that 120*p+1 is a perfect square. - Lamine Ngom, Jul 22 2023

Crossrefs

Cf. A057570, A154293, A154297, A154298, A154299, A154300, A154301, A154302, A154303, A154304.

Programs

Mathematica

lst={};s=0;Do[s+=n/15;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,9!}];lst
Select[(Accumulate[Range[200]])/15,PrimeQ] (* Harvey P. Dale, Oct 30 2011 *)

PARI

select(x->denominator(x)==1 & isprime(x), vector(30,m,m^2+m)/30)  \\ M. F. Hasler, Dec 31 2012

Extensions

Edited by M. F. Hasler, Dec 31 2012