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

A154304 Primes of the form (1+2+...+m)/210 = A000217(m)/210.

Original entry on oeis.org

3, 17, 47, 419, 421
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=210.
The corresponding m-values are m=35,84,140,419,420. It is clear that for m>420, T(m)/210 = m(m+1)/420 cannot be a prime, since then each factor in the numerator is larger than the denominator. 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

Crossrefs

Cf. A057570, A154293, A154296 - A154303.

Programs

  • Mathematica
    lst={};s=0;Do[s+=n/210;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,6*9!}];lst
  • PARI
    A154304(d=210)={select(x->denominator(x)==1 && isprime(x), vector(d*=2, m, m^2+m)/d)}  \\ - M. F. Hasler, Jan 06 2013

Extensions

Edited by M. F. Hasler, Jan 06 2013

A154297 Primes of the form (1+2+3+...+m)/21 = A000217(m)/21, for some m.

Original entry on oeis.org

5, 11, 41, 43
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 06 2009

Keywords

Comments

This asks for primes p which are a triangular number divided by 21, or, 2*3*7*p=k*(k+1) for some k. Matching factors shows that the sequence is complete [R. J. Mathar, Aug 15 2010]
Original definition: Primes of the form : 1/x+2/x+3/x+4/x+5/x+6/x+7/x+..., x=21.
The corresponding m-values are m=14, 21, 41, 42 (cf. A154296). It is clear that for m>42, A000217(m)/21 = m(m+1)/42 cannot be a prime. - M. F. Hasler, Dec 31 2012

Crossrefs

Cf. A057570, A154293, A154296, A154298, A154299, A154300, A154301, A154302, A154303, A154304.

Programs

  • Mathematica
    lst={};s=0;Do[s+=n/21;If[Floor[s]==s,If[PrimeQ[s],AppendTo[lst,s]]],{n,0,9!}];lst
#/21&/@Select[Accumulate[Range[100]],PrimeQ[#/21]&] (* Harvey P. Dale, Dec 17 2012 *)
  • PARI
    select(x->denominator(x)==1 & isprime(x), vector(42, m, m^2+m)/42)  \\ - M. F. Hasler, Dec 31 2012

Extensions

Added keywords fini,full - R. J. Mathar, Aug 15 2010
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.

Content is available under The OEIS End-User License Agreement.