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

3, 7, 29, 31

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=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

Links

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A018989 A325258 A073126 * A038900 A068485 A019352

Adjacent sequences: A154293 A154294 A154295 * A154297 A154298 A154299

Keyword

nonn,fini,full,easy

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Extensions

Edited by M. F. Hasler, Dec 31 2012

Status

approved