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 1-5 of 5 results.

A086709 Primes p such that p-1 and p+1 are both divisible by fourth powers.

Original entry on oeis.org

1249, 2753, 3727, 4049, 4801, 5023, 7937, 10529, 11503, 12799, 13121, 15391, 20897, 21871, 22193, 23167, 25759, 28351, 28751, 31249, 32561, 33857, 35153, 37423, 39041, 42929, 46817, 47791, 48751, 49409, 50383, 51679, 55889, 58481, 62047
Offset: 1

Views

Author

Amarnath Murthy, Jason Earls, Jul 28 2003

Keywords

Links

Crossrefs

Cf. A046101, A075432, A086708, A089212.

Programs

  • Mathematica
    f[n_]:=Max[Last/@FactorInteger[n]]; lst={};Do[p=Prime[n];If[f[p-1]>=4&&f[p+1]>=4,AppendTo[lst,p]],{n,8!}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 03 2009 *)
dfpQ[n_]:=Max[Transpose[FactorInteger[n]][[2]]]>3; Select[Prime[Range[ 6500]], dfpQ[#-1]&&dfpQ[#+1]&] (* Harvey P. Dale, May 11 2012 *)

A166003 Primes p such that p+-1, p+-2 and p+-3 are not squarefree.

Original entry on oeis.org

47527, 186247, 218527, 245149, 269953, 377543, 390449, 432277, 447823, 453053, 469649, 518123, 568177, 584911, 589273, 606323, 632347, 661547, 761347, 831751, 848213, 897577, 913327, 925949, 952253, 1172351, 1205647, 1220347, 1241477
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Oct 03 2009

Keywords

Links

Crossrefs

Cf. A086708, A086709, A089199, A089200, A089212, A166000, A166001, A166002.

Programs

  • Mathematica
    f[n_]:=Max[Last/@FactorInteger[n]]; q=2;lst={};Do[p=Prime[n];If[f[p-3]>=q&&f[p-2]>=q&&f[p-1]>=q&&f[p+1]>=q&&f[p+2]>=q&&f[p+3]>=q,AppendTo[lst,p]],{n,6*8!}];lst
Select[Prime[Range[100000]],NoneTrue[#+{-3,-2,-1,1,2,3},SquareFreeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 17 2018 *)

Extensions

Edited by N. J. A. Sloane, Oct 04 2009

A166000 Primes p such that p-5, p-3, p+3, and p+5 are divisible by cubes.

Original entry on oeis.org

12253, 14747, 65173, 83003, 93253, 95747, 109139, 147253, 176747, 213349, 255253, 282253, 284747, 287437, 305267, 311747, 315517, 336253, 338747, 364699, 365747, 444253, 452579, 471253, 525253, 554747, 583789, 633253, 716747, 741253, 743747
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Oct 03 2009

Keywords

Comments

Subsequence of A089201. - R. J. Mathar, Dec 08 2015
Contains all primes == 12253 (mod 27000), and therefore the sequence is infinite. - Robert Israel, Apr 21 2016

Links

Crossrefs

Cf. A089201, A086708, A086709, A089212, A046099.

Programs

  • Maple
    filter:= proc(p) local d;
  if not isprime(p) then return false fi;
  for d in [-5,-3,3,5] do
     if max(map(t -> t[2], ifactors(p+d)[2])) < 3 then return false fi;
  od;
  true
end proc:
select(filter, [seq(t,t=7..10^6,2)]); # Robert Israel, Apr 21 2016
# alternative
isA166000 := proc(n)
    if isprime(n) then
            isA046099(n-3) and isA046099(n+3) and isA046099(n-5) and isA046099(n+5) ;
    else
            false;
    end if;
end proc: # R. J. Mathar, Aug 14 2024
  • Mathematica
    f[n_]:=Max[Last/@FactorInteger[n]]; q=3;lst={};Do[p=Prime[n];If[f[p-5]>=q&&f[p-3]>=q&&f[p+3]>=q&&f[p+5]>=q,AppendTo[lst,p]],{n,4*8!}];lst
  • PARI
    ncf(n)={vecmax(factor(n)[,2])>2};forprime(p=5,1e7,if(ncf(p+5)&&ncf(p+3)&&ncf(p-3)&&ncf(p-5),print1(p","))) /* Charles R Greathouse IV, Oct 05 2009 */

A166001 Primes p such that p-5, p-4, p+4, and p+5 are each divisible by a cube > 1.

Original entry on oeis.org

751379, 2414507, 2839621, 3170371, 4469629, 5736371, 21154909, 22556371, 22991629, 23313371, 23748629, 24338371, 28372621, 31628371, 32079757, 33009629, 41078371, 42270629, 43465307, 44446621, 49746667, 50579339
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Oct 03 2009

Keywords

Links

Crossrefs

Cf. A086708, A086709, A089199, A089200, A089212, A166000.

Programs

  • Mathematica
    f[n_]:=Max[Last/@FactorInteger[n]]; q=3;lst={};Do[p=Prime[n];If[f[p-5]>=q&&f[p-4]>=q&&f[p+4]>=q&&f[p+5]>=q,AppendTo[lst,p]],{n,4*8!}];lst

Extensions

Extended by Charles R Greathouse IV, Oct 09 2009

A166002 Primes p such that p-6, p-5, p+5, and p+6 are each divisible by a cube greater than 1.

Original entry on oeis.org

1934869, 6136619, 11195869, 11845499, 12385381, 33919619, 39139381, 39790381, 52937869, 53209381, 53631131, 54601619, 58690381, 62892131, 67951381, 77212381, 80224619, 88874869, 94544869, 95734381, 99936131, 103805869, 108827869
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Oct 03 2009

Keywords

Crossrefs

Cf. A086708, A086709, A089199, A089200, A089212, A166000, A166001

Programs

  • Mathematica
    f[n_]:=Max[Last/@FactorInteger[n]]; q=3;lst={};Do[p=Prime[n];If[f[p-6]>=q&&f[p-5]>=q&&f[p+5]>=q&&f[p+6]>=q,AppendTo[lst,p]],{n,5*9!}];lst

Extensions

Edited by N. J. A. Sloane, Oct 04 2009
Extended and edited by Charles R Greathouse IV, May 12 2010
Showing 1-5 of 5 results.

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

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