cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

3, 7, 29, 31
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Keywords

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

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

Original entry on oeis.org

3, 13, 29, 113
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Keywords

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

Crossrefs

Cf. A057570, A154293, A154296 - A154304.

Programs

  • 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 *)
  • 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

Extensions

Keywords fini,full added by R. J. Mathar, Aug 15 2010
Edited by M. F. Hasler, Jan 06 2013

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

Original entry on oeis.org

2, 7, 17, 67
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Keywords

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
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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