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.

A242059 lpf_3(A242057(n)-1), where lpf_3(n) = lpf(n/3^t) (cf. A020639) such that 3^t (t>=0) is the maximal power of 3 which divides n.

Original entry on oeis.org

1, 5, 7, 5, 1, 11, 5, 13, 5, 7, 5, 7, 5, 23, 5, 1, 5, 7, 5, 11, 5, 37, 5, 7, 5, 43, 7, 5, 47, 11, 5, 17, 5, 53, 7, 5, 13, 5, 61, 5, 7, 5, 67, 7, 5, 11, 71, 5, 13, 5, 7, 5, 1, 11, 5, 7, 5, 7, 5, 31, 5, 5, 7, 5, 103, 5, 11, 17, 5, 7, 37, 5, 113, 11, 7, 5, 13, 5
Offset: 1

Views

Author

Vladimir Shevelev, Aug 13 2014

Keywords

Comments

An analog of A242033.

Links

Crossrefs

Cf. A245024, A243937, A242057, A242058, A242033, A242034, A020639.

Programs

  • Mathematica
    lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]];
lpf3[n_]:=lpf3[n]=If[#==1,1,lpf[#]]&[n/3^IntegerExponent[n,3]]
Map[lpf3[#-1]&,Select[Range[4,300,2],lpf3[#-1]Peter J. C. Moses, Aug 13 2014 *)
  • PARI
    lpf3(n)=m=n/3^valuation(n, 3); if(m>1, factor(m)[1,1], 1)
apply(n->lpf3(n-1), select(n->lpf3(n-1)Jens Kruse Andersen, Aug 19 2014

Extensions

More terms from Peter J. C. Moses, Aug 13 2014

A242058 Even numbers n for which lpf_3(n-1) > lpf_3(n-3), where lpf_3(n) = lpf(n/3^t) (cf. A020639) such that 3^t (t>=0) is the maximal power of 3 which divides n.

Original entry on oeis.org

6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 52, 54, 58, 60, 62, 68, 72, 74, 78, 80, 84, 88, 90, 94, 98, 102, 104, 108, 110, 114, 118, 122, 124, 128, 132, 138, 140, 148, 150, 152, 158, 164, 168, 172, 174, 178, 180, 182, 188, 192, 194, 198, 200, 208, 212
Offset: 1

Views

Author

Vladimir Shevelev, Aug 13 2014

Keywords

Comments

An analog of A243937.

Links

Crossrefs

Cf. A245024, A243937, A242057, A020639.

Programs

  • Mathematica
    lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]];
lpf3[n_]:=lpf3[n]=If[#==1,1,lpf[#]]&[n/3^IntegerExponent[n,3]]
Select[Range[4,300,2],lpf3[#-1]>lpf3[#-3]&] (* Peter J. C. Moses, Aug 13 2014 *)
  • PARI
    lpf3(n)=m=n/3^valuation(n, 3); if(m>1, factor(m)[1,1], 1)
select(n->lpf3(n-1)>lpf3(n-3), vector(200, x, 2*x)) \\ Jens Kruse Andersen, Aug 19 2014

Extensions

More terms from Peter J. C. Moses, Aug 13 2014

A242060 Lpf_3(A242058(n)-3), where lpf_3(n) = lpf(n/3^t) (cf. A020639) such that 3^t (t>=0) is the maximal power of 3 which divides n.

Original entry on oeis.org

1, 5, 1, 11, 5, 17, 7, 1, 29, 5, 13, 41, 5, 7, 17, 5, 19, 59, 5, 23, 71, 5, 7, 1, 5, 29, 7, 5, 11, 101, 5, 107, 37, 5, 7, 11, 5, 43, 5, 137, 5, 7, 149, 5, 7, 5, 13, 19, 5, 59, 179, 5, 7, 191, 5, 197, 5, 11, 5, 7, 13, 5, 227, 7, 5, 79, 239, 1, 5, 13, 83, 5, 7
Offset: 1

Views

Author

Vladimir Shevelev, Aug 13 2014

Keywords

Comments

An analog of A242034. Records are lesser numbers of twin primes.

Crossrefs

Cf. A245024, A243937, A242057, A242058, A242059, A242033, A242034.

Programs

  • Mathematica
    lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]];
lpf3[n_]:=lpf3[n]=If[#==1,1,lpf[#]]&[n/3^IntegerExponent[n,3]]
Map[lpf3[#-3]&,Select[Range[4,300,2],lpf3[#-1]>lpf3[#-3]&]](* Peter J. C. Moses, Aug 13 2014 *)

Extensions

More terms from Peter J. C. Moses, Aug 13 2014

A242065 Smallest k such that the union of {A242059(i): 1 <= i <= k} and {A242060(i): 1 <= i <= k} includes all primes {5, ..., prime(n)}.

Original entry on oeis.org

2, 3, 4, 8, 8, 17, 17, 17, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 179, 179, 179, 179, 179, 179, 179, 179, 264, 264, 264, 319, 319, 319, 319, 365, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 1112, 4372, 4372, 4372, 4372, 4372, 15504, 15504
Offset: 3

Views

Author

Vladimir Shevelev, Aug 13 2014

Keywords

Crossrefs

Cf. A242033, A242034, A242036, A242037, A242057, A242058, A242059, A242060, A242064.

Programs

  • Mathematica
    lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]];(*least prime factor*)
lpf3[n_]:=lpf3[n]=If[#==1,1,lpf[#]]&[n/3^IntegerExponent[n,3]];
A242059=Map[lpf3[#-1]&,Select[Range[4,100000,2],lpf3[#-1]A242057*)];
A242060=Map[lpf3[#-3]&,Select[Range[4,100000,2],lpf3[#-1]>lpf3[#-3]&](*A242058*)];
pos={};NestWhile[#+1&,3,(AppendTo[pos,Min[Position[A242059,Prime[#],1,1],Position[A242060,Prime[#],1,1]/.{}->0]];!Last[pos]==0)&];
A242065=Rest[FoldList[Max,-Infinity,Flatten[pos]]] (* Peter J. C. Moses, Aug 14 2014 *)

Extensions

More terms from Peter J. C. Moses, Aug 14 2014

A242066 The smallest even k such that lpf_3(k-3) > lpf_3(k-1) >= p_n, where lpf_3(n) = lpf(n/3^t) (cf. A020639) such that 3^t (t>=0) is the maximal power of 3 which divides n.

Original entry on oeis.org

16, 22, 34, 40, 70, 70, 70, 112, 112, 112, 130, 130, 142, 160, 184, 184, 202, 214, 310, 310, 310, 310, 310, 310, 310, 340, 340, 340, 382, 412, 412, 490, 490, 490, 490, 490, 502, 544, 544, 544, 574, 580, 634, 634, 634, 754, 754, 754, 754, 754, 754, 754, 772
Offset: 3

Views

Author

Vladimir Shevelev, Aug 13 2014

Keywords

Comments

a(n)-3 and (a(n)-1)/3 are primes.

Crossrefs

Cf. A242057, A242058, A242059, A242060, A242064, A242065, A242033, A242034, A242036, A242037.

Programs

  • Mathematica
    lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]];(*least prime factor*)
lpf3[n_]:=lpf3[n]=If[#==1,1,lpf[#]]&[n/3^IntegerExponent[n,3]];
Table[NestWhile[#+2&,2,!(lpf3[#-3]>lpf3[#-1]>=Prime[n])&],{n,3,100}] (* Peter J. C. Moses, Aug 14 2014 *)
Showing 1-5 of 5 results.

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