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.

Previous Showing 41-48 of 48 results.

A192647 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2 - y^2 > 0 then x^2 - y^2 is in S, and 1 and 3 are in S.

Original entry on oeis.org

1, 3, 8, 55, 63, 944, 2961, 3016, 3024, 3905, 3960, 3968, 48320, 63424, 328735, 377055, 432575, 495999, 887167, 888111, 891072, 891127, 891135, 6104449, 6152769, 6481504, 6537024, 6585344, 6600448, 6648768, 6914079, 6977503, 7876385, 8205120
Offset: 1

Views

Author

Clark Kimberling, Jul 06 2011

Keywords

Comments

See A192645.

Links

Crossrefs

Cf. A192476, A192646.

Programs

  • Mathematica
    start = {1, 3};
f[x_, y_] := If[MemberQ[Range[1, 500000], x^2 - y^2], x^2 - 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}]]]], # <
      500000 &]];
t = FixedPoint[b, start]  (* A192647 *)

A192648 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2-y^2>0 then x^2-y^2 is in S, and 2 and 3 are in S.

Original entry on oeis.org

2, 3, 5, 16, 21, 185, 231, 247, 252, 416, 432, 437, 2495, 4345, 7648, 10143, 13568, 17913, 19136, 26784, 29279, 33784, 33969, 34200, 34216, 34221, 52920, 53105, 53336, 53352, 53357, 60568, 60753, 60984, 61000, 61005, 63063, 63248, 63479
Offset: 1

Views

Author

Clark Kimberling, Jul 06 2011

Keywords

Comments

See A192645.

Links

Crossrefs

Cf. A192476, A192646.

Programs

  • Mathematica
    start = {2, 3};
f[x_, y_] := If[MemberQ[Range[1, 150000], x^2 - y^2], x^2 - 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}]]]], # <
      150000 &]];
t = FixedPoint[b, start]  (* A192648 *)

A192534 (A192533)/2.

Original entry on oeis.org

1, 2, 6, 8, 56, 62, 72, 104, 114, 128, 5504, 5672, 6056, 6162, 6272, 6824, 7016, 7448, 7566, 7688, 8576, 9128, 9344, 9576, 10088, 10226, 10368, 16256, 16424, 17024, 19496, 19544, 19944, 20096, 20456, 21224, 21426, 21632, 23912, 24296, 24584
Offset: 1

Views

Author

Clark Kimberling, Jul 04 2011

Keywords

Comments

See A192533.

Crossrefs

Cf. A192476, A192533.

Programs

A192538 (A192537)/2.

Original entry on oeis.org

1, 3, 17, 27, 545, 563, 867, 1395, 1433, 1577, 2187, 580793, 585363, 592433, 593507, 620195, 624945, 632267, 633377, 891075, 921153, 950907, 1481427, 1489217, 1500795, 1502513, 1624913, 1649195
Offset: 1

Views

Author

Clark Kimberling, Jul 04 2011

Keywords

Comments

See A192537.

Crossrefs

Cf. A192476, A192537.

Programs

A192589 Monotonic ordering of set S generated by these rules: if x and y are in S and xy+3 is a prime, then xy+3 is in S, and 2 and 4 are in S.

Original entry on oeis.org

2, 4, 7, 11, 17, 19, 31, 37, 41, 47, 71, 79, 97, 127, 151, 167, 191, 197, 257, 337, 397, 607, 677, 797, 1031, 1217, 1597, 2437, 2711, 3191, 4127, 4871, 4877, 10847, 43391
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192476 and A192580.

Programs

  • Mathematica
    start = {2, 4}; primes = Table[Prime[n], {n, 1, 40000}];
f[x_, y_] := If[MemberQ[primes, x*y + 3], x*y + 3]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      200000 &]];
t = FixedPoint[b, start]    (* A192589 *)

A192590 Monotonic ordering of set S generated by these rules: if x and y are in S and xy-3 is a prime, then xy-3 is in S, and 2 and 4 are in S.

Original entry on oeis.org

2, 4, 5, 7, 11, 13, 17, 19, 23, 31, 41, 43, 59, 73, 79, 83, 89, 163, 233, 313, 353, 463, 929, 1249, 1409, 4993
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192476, A192580.

Programs

  • Mathematica
    start = {2, 4}; primes = Table[Prime[n], {n, 1, 40000}];
f[x_, y_] := If[MemberQ[primes, x*y - 3], x*y - 3]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      200000 &]];
t = FixedPoint[b, start]    (* A192590 *)

A192591 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2+y^2+1 is a prime, then x^2+y^2+1 is in S, and 1 is in S.

Original entry on oeis.org

1, 3, 11, 19, 131
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192476, A192580.

Programs

  • Mathematica
    start = {1}; primes = Table[Prime[n], {n, 1, 40000}];
f[x_, y_] := If[MemberQ[primes, x^2 + y^2 + 1], x^2 + y^2 + 1]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      200000 &]];
t = FixedPoint[b, start]    (* A192591 *)

A192595 Index-list of the primes generated at A192594.

Original entry on oeis.org

0, 4, 8, 12, 14, 21, 22, 25, 29, 36, 38, 42, 44, 46, 48, 50, 53, 58, 63, 65, 67, 68, 73, 74, 75, 78, 80, 82, 84, 85, 88, 90, 93, 95, 99, 100, 101, 105, 106, 110, 112, 114, 115, 117, 121, 122, 125, 127, 129, 131, 133, 134, 136, 138, 141, 143, 145, 147, 149, 151
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

The initial 1 is given an index of 0. All other terms of A192594 are primes: 7=p(4), 19=p(8), etc.

Crossrefs

Cf. A192476, A192580, A192594.

Programs

Previous Showing 41-48 of 48 results.

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