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.

A364309 Numbers k such that k, k+1 and k+2 have exactly 4 distinct prime factors.

Original entry on oeis.org

37960, 44484, 45694, 50140, 51428, 55130, 55384, 61334, 63364, 64294, 67164, 68264, 68474, 70004, 70090, 71708, 72708, 76152, 80444, 81548, 81718, 82040, 84434, 85490, 86240, 90363, 95380, 97382, 98020, 99084, 99384, 99428, 99788, 100164, 100490, 100594, 102254, 102542, 104804, 105994, 108204
Offset: 1

Views

Author

R. J. Mathar, Jul 18 2023

Keywords

Examples

			37960 = 2^3*5*13*73, 37961 = 7*11*17*29, and 37962 = 2*3^3*19*37 each have 4 distinct prime factors, so 37960 is in the sequence.

Links

Crossrefs

Subsequence of A006073 and of A140078.
A176167 is a subsequence.
Cf. A364307 (2 factors), A364308 (3 factors), A364266 (5 factors), A364265 (6 factors), A001221, A087966, A168628.

Programs

  • Mathematica
    q[n_] := q[n] = PrimeNu[n] == 4; Select[Range[10^5], q[#] && q[#+1] && q[#+2] &] (* Amiram Eldar, Oct 01 2024 *)

Formula

a(1) = A087966(3).
a(n)+1 = A168628(n).
{k: A001221(k) = A001221(k+1) = A001221(k+2) = 4}.

A168629 Numbers n such that n,n+1 and sum of this two numbers have at least 3 distinct prime factors.

Original entry on oeis.org

1105, 1130, 1462, 1644, 1742, 1767, 2014, 2222, 2232, 2260, 2337, 2365, 2397, 2464, 2541, 2667, 2684, 2697, 2702, 2755, 2821, 2914, 3074, 3115, 3195, 3289, 3332, 3477, 3484, 3514, 3552, 3619, 3657, 3685, 3782, 3783, 3842, 3965, 4014, 4088, 4122, 4147, 4277
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 01 2009

Keywords

Examples

			1105 = 5*13*17, 1106 = 2*7*79, 1105 + 1106 = 2211 = 3*11*67.

Crossrefs

Cf. A140077, A140078, A168626, A168628.

Programs

  • Maple
    q:= n-> andmap(x-> nops(numtheory[factorset](x))>2, [n, n+1, 2*n+1]):
select(q, [$1..4600])[];  # Alois P. Heinz, Jun 29 2021
  • Mathematica
    f[n_]:=Length[FactorInteger[n]]; lst={};Do[If[f[n]>=3&&f[n+1]>=3&&f[n+n+1]>=3,AppendTo[lst,n]],{n,8!}];lst

A168630 Numbers n such that n, n+1, and the sum of those two numbers each have 4 or more distinct prime factors.

Original entry on oeis.org

46189, 50634, 69597, 76797, 90117, 97954, 108205, 115804, 127347, 138957, 144627, 159340, 164020, 166022, 166497, 166705, 167205, 167485, 173194, 174454, 181670, 186294, 190014, 193154, 198789, 211029, 212134, 214225, 217217, 221815, 222547, 224146
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 01 2009

Keywords

Examples

			FactorInteger[46189]=11*13*17*19, FactorInteger[46190]=2*5*31*149, FactorInteger[46189+46190]=3*7*53*83,..

Links

Crossrefs

Cf. A140077, A140078, A168626, A168628, A168629

Programs

  • Maple
    g:= proc(n) option remember; nops(numtheory:-factorset(n))>=4 end proc:
filter:= n -> g(n) and g(n+1) and g(2*n+1):
select(filter, [$1..300000]); # Robert Israel, May 09 2018
  • Mathematica
    f[n_]:=Length[FactorInteger[n]]; lst={};Do[If[f[n]>=4&&f[n+1]>=4&&f[n+n+1]>=4,AppendTo[lst,n]],{n,9!}];lst
Select[Range[225000],Min[Thread[PrimeNu[{#,#+1,2#+1}]]]>3&](* Harvey P. Dale, Nov 11 2017 *)

Extensions

Definition modified and terms extended by Harvey P. Dale, Nov 11 2017
Showing 1-3 of 3 results.

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

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