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.

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A192525 Monotonic ordering of set S generated by these rules: if x and y are in S then 2xy-x-y is in S, and 3 is in S.

Original entry on oeis.org

3, 12, 57, 264, 282, 1299, 1317, 1407, 6060, 6384, 6474, 6492, 6582, 7032, 29775, 29865, 30279, 30297, 31809, 31917, 32349, 32367, 32457, 32907, 35157, 138864, 139368, 146730, 146820, 148350, 148764, 148872, 148890, 149304, 149322, 151374
Offset: 1

Views

Author

Clark Kimberling, Jul 03 2011

Keywords

Crossrefs

Cf. A192476.

Programs

  • Mathematica
    start = {3}; f[x_, y_] := 2 x*y - x - y
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      500000 &]];
t = NestList[b, start, 12][[-1]] (* A192525 *)
t/3 (* A192526 *)
Table[t[[i]] - t[[i - 1]], {i, 2, Length[t]}]  (* differences *)

A192531 Monotonic ordering of set S generated by these rules: if x and y are in S then 3xy-2x-2y is in S, and 2 is in S.

Original entry on oeis.org

2, 4, 12, 32, 44, 112, 124, 172, 312, 384, 432, 444, 492, 684, 1064, 1112, 1232, 1244, 1472, 1532, 1712, 1724, 1772, 1964, 2732, 2944, 3112, 3784, 3832, 4072, 4192, 4252, 4312, 4432, 4444, 4912, 4924, 4972, 5632, 5824, 5884, 6124, 6832, 6844, 6892
Offset: 1

Views

Author

Clark Kimberling, Jul 04 2011

Keywords

Comments

See A192476.

Crossrefs

Cf. A192476, A192532.

Programs

  • Mathematica
    start = {2}; f[x_, y_] := 3 x*y - 2 x - 2 y
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      30000 &]];
t = FixedPoint[b, start] (* A192531 *)
t/2   (* A192532 *)

A192533 Monotonic ordering of set S generated by these rules: if x and y are in S then x^2+y^2-xy is in S, and 2 is in S.

Original entry on oeis.org

2, 4, 12, 16, 112, 124, 144, 208, 228, 256, 11008, 11344, 12112, 12324, 12544, 13648, 14032, 14896, 15132, 15376, 17152, 18256, 18688, 19152, 20176, 20452, 20736, 32512, 32848, 34048, 38992, 39088, 39888, 40192, 40912, 42448, 42852, 43264
Offset: 1

Views

Author

Clark Kimberling, Jul 04 2011

Keywords

Comments

See A192476.

Crossrefs

Cf. A192476, A192534.

Programs

  • Mathematica
    start = {2}; f[x_, y_] := x^2 + y^2 - x*y
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      80000 &]];
t = FixedPoint[b, start] (* A192533 *)
t/2 (* A192534 *)

A192537 Monotonic ordering of set S generated by these rules: if x and y are in S then x^2+y^2-xy/2 is in S, and 2 is in S.

Original entry on oeis.org

2, 6, 34, 54, 1090, 1126, 1734, 2790, 2866, 3154, 4374, 1161586, 1170726, 1184866, 1187014, 1240390, 1249890, 1264534, 1266754, 1782150, 1842306, 1901814, 2962854, 2978434, 3001590, 3005026, 3249826, 3298390
Offset: 1

Views

Author

Clark Kimberling, Jul 04 2011

Keywords

Comments

See A192476.

Crossrefs

Cf. A192476, A192538.

Programs

  • Mathematica
    start = {2}; f[x_, y_] := x^2 + y^2 - x*y/2
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      4000000 &]];
t = FixedPoint[b, start] (* A192537 *)
t/2 (* A192538 *)

A192582 Monotonic ordering of set S generated by these rules: if x and y are in S and xy+1 is a prime, then xy+1 is in S, and 2, 4, and 6 are in S.

Original entry on oeis.org

2, 4, 5, 6, 11, 13, 17, 23, 31, 37, 47, 53, 67, 79, 103, 107, 139, 149, 223, 269, 283, 317, 557, 619, 643, 1699, 2477, 3343
Offset: 1

Views

Author

Clark Kimberling, Jul 04 2011

Keywords

Comments

See the discussion at A192580.

Crossrefs

Cf. A192476.

Programs

  • Mathematica
    start = {2, 4, 6}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, x*y + 1], x*y + 1]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      10000000 &]];
t = FixedPoint[b, start]  (* A192582 *)

A192584 Monotonic ordering of set S generated by these rules: if x and y are in S and xy+1 is a prime, then xy+1 is in S, and 2, 4, 6, 8, and 10 are in S.

Original entry on oeis.org

2, 4, 5, 6, 8, 10, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 79, 83, 89, 101, 103, 107, 131, 137, 139, 149, 167, 179, 223, 263, 269, 283, 311, 317, 359, 367, 499, 557, 607, 619, 643, 719, 787, 809, 823, 857, 1031, 1049, 1097, 1193, 1433, 1439, 1579, 1619
Offset: 1

Views

Author

Clark Kimberling, Jul 04 2011

Keywords

Comments

See the discussions at A192580 and A192584. The number of terms in this finite sequence is 104. The greatest term is 15845273.

Links

Crossrefs

Cf. A192476, A192580, A192583.

Programs

  • Mathematica
    start = {2, 4, 6, 8, 10}; seq = {}; new = start; While[new != {},
seq = Union[seq, new]; fresh = new; new = {}; Do[If[PrimeQ[u = x*y + 1], If[! MemberQ[seq, u], AppendTo[new, u]]], {x, seq}, {y, fresh}]]; seq (* Giovanni Resta, Mar 21 2013 *)

Extensions

Corrected by Giovanni Resta, Mar 21 2013

A192586 Monotonic ordering of set S generated by these rules: if x and y are in S and xy-1 is a prime, then xy-1 is in S, and 2 and 4 are in S.

Original entry on oeis.org

2, 3, 4, 5, 7, 11, 13, 19, 37, 43, 73
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192476, A192580, A192587, A192588.

Programs

  • Mathematica
    start = {2, 4}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, x*y - 1], x*y - 1]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      50000 &]];
t = FixedPoint[b, start]  (* A192586 *)

A192587 Monotonic ordering of set S generated by these rules: if x and y are in S and xy-1 is a prime, then xy-1 is in S, and 2, 4, and 6 are in S.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, 67, 73, 101, 113, 137, 163, 173, 257, 401, 547, 677, 691, 821, 977, 1093, 1381, 2707, 3907, 5413, 5861
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192476, A192580, A192586, A192588.

Programs

  • Mathematica
    start = {2, 4, 6}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, x*y - 1], x*y - 1]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      50000 &]];
t = FixedPoint[b, start]   (* A192587 *)

A192588 Monotonic ordering of set S generated by these rules: if x and y are in S and xy-1 is a prime, then xy-1 is in S, and 2, 4, 6, and 8 are in S.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 61, 67, 73, 101, 103, 113, 137, 151, 163, 173, 257, 281, 401, 487, 547, 617, 677, 691, 821, 823, 977, 1093, 1123, 1303, 1381, 2467, 2707, 3701, 3907, 4933, 4937, 5413, 5527, 5861, 6737, 7817
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.
Last term is a(61) = 62533. - Giovanni Resta, Mar 21 2013

Links

Crossrefs

Cf. A192476, A192580, A192586, A192587.

Programs

  • Mathematica
    start = {2, 4, 6, 8}; seq = {}; new = start; While[new != {}, seq = Union[seq, new]; fresh = new; new = {}; Do[If[PrimeQ[u = x*y - 1], If[! MemberQ[seq, u], AppendTo[new, u]]], {x, seq}, {y, fresh}]]; seq (* Giovanni Resta, Mar 21 2013 *)

A192592 Monotonic ordering of set S generated by these rules: if x and y are in S and 3x+2y is a prime, then 3x+2y is in S, and 1 is in S.

Original entry on oeis.org

1, 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 401, 409, 421, 433, 449, 457, 461, 509, 521, 541, 557, 569, 577, 593, 601, 613, 617
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.

Links

Crossrefs

Cf. A192476, A192580, A192593.

Programs

  • Mathematica
    start = {1}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, 2 x + 3 y], 2 x + 3 y]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,
         Length[w]}]]]], # < 1000 &]];
t = FixedPoint[b, start]     (* A192592 *)
PrimePi[t]    (* A192593 *)
Previous Showing 11-20 of 48 results. Next

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