A192476 -id:A192476 - cp's OEIS frontend

A192598 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2+2y^2 is a prime, then x^2+2y^2 is in S, and 1 is in S.

1, 3, 11, 19, 139, 251, 379

Offset: 1

Clark Kimberling, Jul 05 2011

See the discussions at A192476 and A192580. The start-set for A192598 is {1}. For results using start-sets {1,2}, and {1,2,4}, see A192612 and A192613.

Cf. A192476, A192580, A192612, A192613.

start = {1}; primes = Table[Prime[n], {n, 1, 20000}];
f[x_, y_] := If[MemberQ[primes, x^2 + 2 y^2], x^2 + 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,
         Length[w]}]]]], # < 30000 &]];
t = FixedPoint[b, start]  (* A192598 *)

A192612 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2+2y^2 is a prime, then x^2+2y^2 is in S, and 1 and 2 are in S.

Original entry on oeis.org

1, 2, 3, 11, 17, 19, 139, 251, 307, 379, 587

Offset: 1

Clark Kimberling, Jul 05 2011

See the discussions at A192476 and A192580. The start-set for A192612 is {1,2}. For results using start-sets {1}, and {1,2,4}, see A192598 and A192613.

Cf. A192476, A192580, A192613.

start = {1, 2}; primes = Table[Prime[n], {n, 1, 20000}];
f[x_, y_] := If[MemberQ[primes, x^2 + 2 y^2], x^2 + 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,
         Length[w]}]]]], # < 30000 &]];
t = FixedPoint[b, start]  (* A192612 *)

A192613 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2+2y^2 is a prime, then x^2+2y^2 is in S, and 1, 2, and 4 are in S.

Original entry on oeis.org

1, 2, 3, 4, 11, 17, 19, 41, 139, 251, 307, 379, 587, 1699, 3371

Offset: 1

Clark Kimberling, Jul 05 2011

See the discussions at A192476 and A192580.

Cf. A192612, A192476, A192580.

start = {1, 2, 4}; primes = Table[Prime[n], {n, 1, 20000}];
f[x_, y_] := If[MemberQ[primes, x^2 + 2 y^2], x^2 + 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,
         Length[w]}]]]], # < 30000 &]];
t = FixedPoint[b, start] (* A192613 *)

A192615 Index-list of the primes generated at A192614.

Original entry on oeis.org

0, 2, 4, 5, 9, 11, 15, 20, 27, 31, 36, 39, 43, 56, 64, 76, 83, 96, 115, 118, 132, 150, 154, 156, 163, 166, 185, 190, 213, 236, 250, 253, 276, 281, 282, 283, 286, 315, 329, 344, 349, 360, 363, 372, 377, 390, 423, 434, 448, 512, 524, 536

Offset: 1

Clark Kimberling, Jul 05 2011

nonn

			0 is included at the beginning as a representative of the initial 1.  All the other numbers in A192614 are primes, and their indexes are in A192615; e.g., 3 in A192614 matches 2 in A192615, since p(2)=3.

Cf. A192476, A192580, A192615.

Mathematica
```
(See A192614.)
```

A192649 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, 2, and 4 are in S.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 12, 15, 16, 17, 21, 24, 31, 32, 33, 39, 40, 45, 48, 55, 56, 60, 63, 64, 65, 72, 77, 79, 80, 81, 95, 111, 112, 119, 127, 128, 129, 135, 140, 143, 144, 145, 152, 159, 161, 175, 176, 185, 192, 200, 207, 208, 209, 216, 221, 223, 224, 225, 231

Offset: 1

Clark Kimberling, Jul 06 2011

nonn

See A192645.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A192476, A192646, A192650.

start = {1, 2, 4};
f[x_, y_] := If[MemberQ[Range[1, 700], 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}]]]], # <
      700 &]];
t = FixedPoint[b, start]  (* A192649 *)
Differences[t] (* A192650 *)

A192518 Monotonic ordering of set S generated by these rules: if x and y are in S then (x+1)(y+1) is in S, and 2 is in S.

Original entry on oeis.org

2, 9, 30, 93, 100, 282, 303, 310, 849, 912, 933, 940, 961, 1010, 2550, 2739, 2802, 2823, 2830, 2886, 2914, 3033, 3040, 3110, 3131, 7653, 8220, 8409, 8472, 8493, 8500, 8661, 8745, 8773, 8836, 9102, 9123, 9130, 9333, 9340, 9396, 9410, 9424, 9494

Offset: 1

Clark Kimberling, Jul 03 2011

nonn

See A192476.

Cf. A192476.

start = {2}; f[x_, y_] := (x + 1) (y + 1)
b[z_] :=
  Block[{w = z},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      30000 &]];
t = NestList[b, start, 10][[-1]] (* A192518 *)

A192519 Monotonic ordering of set S generated by these rules: if x and y are in S then floor(x*y/2) is in S, and 3 is in S.

Original entry on oeis.org

3, 4, 6, 8, 9, 12, 13, 16, 18, 19, 24, 26, 27, 28, 32, 36, 38, 39, 40, 42, 48, 52, 54, 56, 57, 58, 60, 63, 64, 72, 76, 78, 80, 81, 84, 85, 87, 90, 94, 96, 104, 108, 112, 114, 116, 117, 120, 121, 123, 126, 127, 128, 130, 135, 141, 144, 152, 156, 160, 162, 168, 169

Offset: 1

Clark Kimberling, Jul 03 2011

nonn

Cf. A192476.

start = {3}; f[x_, y_] := Floor[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}]]]], # <
      400 &]];
t = NestList[b, start, 12][[-1]] (* A192519 *)
Table[t[[i]] - t[[i - 1]], {i, 2, Length[t]}]

A192520 Monotonic ordering of set S generated by these rules: if x and y are in S then floor(x*y/2) is in S, and 5 is in S.

Original entry on oeis.org

5, 12, 30, 72, 75, 180, 187, 432, 450, 467, 1080, 1122, 1125, 1167, 2592, 2700, 2802, 2805, 2812, 2917, 6480, 6732, 6750, 7002, 7005, 7012, 7030, 7292, 15552, 16200, 16812, 16830, 16872, 16875, 17484, 17502, 17505, 17512, 17530, 17575, 18230

Offset: 1

Clark Kimberling, Jul 03 2011

nonn

Cf. A192476.

start = {5}; f[x_, y_] := Floor[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}]]]], # <
      70000 &]];
t = NestList[b, start, 14][[-1]] (* A192520 *)
Table[t[[i]] - t[[i - 1]], {i, 2, Length[t]}]  (* difference sequence *)

A192521 Monotonic ordering of set S generated by these rules: if x and y are in S then floor((x+1)(y+1)/2) is in S, and 2 is in S.

Original entry on oeis.org

2, 4, 7, 12, 19, 20, 30, 31, 32, 46, 48, 49, 50, 52, 70, 73, 75, 76, 77, 79, 80, 82, 84, 106, 111, 114, 115, 117, 120, 121, 122, 124, 125, 127, 128, 130, 132, 136, 160, 168, 172, 174, 177, 181, 183, 184, 185, 187, 188, 189, 190, 192, 193, 195, 196, 199, 200

Offset: 1

Clark Kimberling, Jul 03 2011

nonn

Cf. A192476.

start = {2}; f[x_, y_] := Floor[(x + 1)*(y + 1)/2]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      400 &]];
t = NestList[b, start, 14][[-1]] (* A192521 *)
Table[t[[i]] - t[[i - 1]], {i, 2, Length[t]}]  (* differences *)

A192522 Monotonic ordering of set S generated by these rules: if x and y are in S then floor((x-1)(y-1)/2) is in S, and 5 is in S.

Original entry on oeis.org

5, 8, 14, 24, 26, 45, 46, 50, 80, 84, 87, 88, 90, 98, 149, 154, 157, 158, 162, 166, 171, 172, 174, 178, 194, 264, 276, 286, 287, 290, 292, 296, 301, 304, 306, 311, 312, 314, 318, 322, 330, 339, 340, 342, 346, 354, 386, 506, 513, 517, 518, 526, 535, 539

Offset: 1

Clark Kimberling, Jul 03 2011

nonn

Cf. A192476.

start = {5}; f[x_, y_] := Floor[(x - 1)*(y - 1)/2]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      1500 &]];
t = NestList[b, start, 12][[-1]] (* A192522 *)
Table[t[[i]] - t[[i - 1]], {i, 2, Length[t]}]  (* differences *)

cp's OEIS Frontend

A192598 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2+2y^2 is a prime, then x^2+2y^2 is in S, and 1 is in S.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A192612 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2+2y^2 is a prime, then x^2+2y^2 is in S, and 1 and 2 are in S.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A192613 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2+2y^2 is a prime, then x^2+2y^2 is in S, and 1, 2, and 4 are in S.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A192615 Index-list of the primes generated at A192614.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A192649 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, 2, and 4 are in S.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A192518 Monotonic ordering of set S generated by these rules: if x and y are in S then (x+1)(y+1) is in S, and 2 is in S.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A192519 Monotonic ordering of set S generated by these rules: if x and y are in S then floor(x*y/2) is in S, and 3 is in S.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A192520 Monotonic ordering of set S generated by these rules: if x and y are in S then floor(x*y/2) is in S, and 5 is in S.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A192521 Monotonic ordering of set S generated by these rules: if x and y are in S then floor((x+1)(y+1)/2) is in S, and 2 is in S.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A192522 Monotonic ordering of set S generated by these rules: if x and y are in S then floor((x-1)(y-1)/2) is in S, and 5 is in S.

Views

Author

Keywords

Crossrefs

Programs

Mathematica