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 1-4 of 4 results.

A274349 Products of two distinct Lucas numbers (2,3,4,7,11,18,...).

Original entry on oeis.org

6, 8, 12, 14, 21, 22, 28, 33, 36, 44, 54, 58, 72, 77, 87, 94, 116, 126, 141, 152, 188, 198, 203, 228, 246, 304, 319, 329, 369, 398, 492, 517, 522, 532, 597, 644, 796, 836, 846, 861, 966, 1042, 1288, 1353, 1363, 1368, 1393, 1563, 1686, 2084, 2189, 2204, 2214
Offset: 1

Views

Author

Clark Kimberling, Jun 18 2016

Keywords

Examples

			6 = 2*3, 44 = 4*11.

Links

Crossrefs

Cf. A000032, A274348, A274347, A271354.

Programs

  • Maple
    N:= 10000: # for terms <= N
L:= gfun:-rectoproc({f(n)=f(n-1)+f(n-2),f(0)=2,f(1)=1},f(n),remember):
S:= {}:
for i from 2 do
  u:= L(i);
  if u > N then break fi;
  for j from 0 to i-1 do
    if j = 1 then next fi;
    v:= u*L(j);
    if v > N then break fi;
    S:= S union {v};
od od:
sort(convert(S,list)); # Robert Israel, Jan 01 2021
  • Mathematica
    z = 100; f[n_] := LucasL[n]; f[1] = 2 ;
Take[Sort[Flatten[Table[f[u] f[v], {u, 1, z}, {v, 1, u - 1}]]], z]
Take[Times@@@Subsets[Join[{2},LucasL[Range[2,20]]],{2}]//Union,60] (* Harvey P. Dale, Aug 13 2019 *)

A274347 Products of two distinct Lucas numbers (3,4,7,11,18,...).

Original entry on oeis.org

12, 21, 28, 33, 44, 54, 72, 77, 87, 116, 126, 141, 188, 198, 203, 228, 304, 319, 329, 369, 492, 517, 522, 532, 597, 796, 836, 846, 861, 966, 1288, 1353, 1363, 1368, 1393, 1563, 2084, 2189, 2204, 2214, 2254, 2529, 3372, 3542, 3567, 3572, 3582, 3647, 4092
Offset: 1

Views

Author

Clark Kimberling, Jun 18 2016

Keywords

Comments

L(i)*L(j) = L(i+j) + (-1)^i*L(j-i). - Robert Israel, Sep 02 2019

Examples

			12 = 3*4, 21 = 3*7.

Links

Crossrefs

Cf. A000032, A274348, A274349, A271354.

Programs

  • Maple
    L:= gfun:-rectoproc({f(n+1)=f(n)+f(n-1),f(0)=2,f(1)=1},f(n),remember):
Q:= proc(n) local j; op(sort([seq(L(n)+(-1)^j*L(n-2*j),j=2..(n-1)/2)])) end proc:
map(Q, [$5..20]); # Robert Israel, Sep 02 2019
  • Mathematica
    z = 100; f[n_] := LucasL[n];
Take[Sort[Flatten[Table[f[u] f[v], {u, 2, z}, {v, 2, u - 1}]]], z]

A274353 Number of factors L(i) > 1 of A274280(n), where L = A000032 (Lucas numbers, 1,3,4,...)

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 3, 2, 2, 1, 2, 3, 2, 2, 2, 1, 2, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 2, 1, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 2, 2, 3, 4, 3, 2, 3, 3, 2, 3, 2, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 3, 3, 2, 3, 3, 2, 2, 1, 2, 3, 2
Offset: 1

Views

Author

Clark Kimberling, Jun 18 2016

Keywords

Examples

			The products of distinct Lucas numbers, arranged in increasing order, comprise A274280.  The list begins with 1, 3, 4, 7, 11, 12 = 3*4, so that a(6) = 2.

Links

Crossrefs

Cf. A000032, A274280, A274347, A274348, A160009, A272947, A274354.

Programs

  • Mathematica
    r[1] := 1; r[2] := 3; r[n_] := r[n] = r[n - 1] + r[n - 2];
s = {1}; z = 40; f = Map[r, Range[z]]; Take[f, 10]
Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}];
infQ[n_] := MemberQ[f, n];
a = Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[
Rest[Subsets[Map[#[[1]] &, Select[Map[{#, infQ[#]} &,
Divisors[s[[n]]]], #[[2]] && #[[1]] > 1 &]]]]], {n, 2, 200}];
ans = Join[{{1}}, a]; Take[ans, 8]
w = Map[Length, ans] (* A274353 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A274347 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A274348 *)
(* Peter J. C. Moses, Jun 17 2016 *)

A274350 Products of three distinct Lucas numbers (2,3,4,7,11,18,...).

Original entry on oeis.org

24, 42, 56, 66, 84, 88, 108, 132, 144, 154, 174, 216, 231, 232, 252, 282, 308, 348, 376, 378, 396, 406, 456, 504, 564, 594, 608, 609, 638, 658, 738, 792, 812, 912, 957, 984, 987, 1034, 1044, 1064, 1194, 1276, 1316, 1386, 1476, 1551, 1566, 1592, 1596, 1672
Offset: 1

Views

Author

Clark Kimberling, Jun 18 2016

Keywords

Examples

			24 = 2*3*4, 88 = 2 * 4 * 11.

Crossrefs

Cf. A000032, A274348, A274349, A272949.

Programs

  • Mathematica
    z = 100; f[n_] := LucasL[n]; f[1] = 2 ;
Take[Sort[Flatten[Table[f[u] f[v] f[w], {u, 1, z}, {v, 1, u - 1}, {w, 1, v - 1}]]], z]
Showing 1-4 of 4 results.

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