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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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

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192612, A192476, A192580.

Programs

  • Mathematica
    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

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Examples

			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.

Crossrefs

Cf. A192476, A192580, A192615.

Programs

A192581 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, 4, 5, 11, 17, 23, 47
Offset: 1

Views

Author

Clark Kimberling, Jul 04 2011

Keywords

Comments

See the discussion at A192580. As sets, A192580 lies in A192581, which lies in A192582.

Crossrefs

Cf. A192476, A192580.

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]  (* A192581 *)

A192585 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, 5, 8, 11, and 14 are in S.

Original entry on oeis.org

2, 5, 8, 11, 14, 17, 23, 29, 41, 47, 59, 71, 83, 89, 113, 137, 167, 179, 197, 227, 233, 239, 359, 467, 479, 569, 659, 719, 827, 1097, 1163, 1319, 1433, 1439, 1583, 1913, 2339, 2879, 3167, 3347, 3833, 4679, 5273, 9227, 10067, 11579, 15359, 18713, 20063
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

Last term is a(70) = 15785183. - Giovanni Resta, Mar 21 2013

Links

Crossrefs

Cf. A192476, A192580, A192584.

Programs

  • Mathematica
    start = {2, 5, 8, 11, 14}; 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 *)

A192594 Monotonic ordering of set S generated by these rules: if x and y are in S and 5x+2y is a prime, then 5x+2y is in S, and 1 is in S.

Original entry on oeis.org

1, 7, 19, 37, 43, 73, 79, 97, 109, 151, 163, 181, 193, 199, 223, 229, 241, 271, 307, 313, 331, 337, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 613, 619, 631, 643, 661, 673, 691, 709, 727, 739, 751, 757, 769
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192595, A192476, A192580.

Programs

  • Mathematica
    start = {1}; primes = Table[Prime[n], {n, 1, 1000}];
f[x_, y_] := If[MemberQ[primes, 5 x + 2 y], 5 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,
         Length[w]}]]]], # < 2000 &]];
t = FixedPoint[b, start]    (* A192594 *)
PrimePi[t]    (* A192595 *)

A192596 Monotonic ordering of set S generated by these rules: if x and y are in S and 3x+4y is a prime, then 3x+4y is in S, and 1 is in S.

Original entry on oeis.org

1, 7, 31, 97, 127, 409, 601, 769, 1231, 1657, 1831, 2017, 2311, 3079, 3169, 3457, 3631, 3697, 3943, 4201, 4999, 5479, 5521, 5881, 6079, 6151, 6607, 6961, 7057, 7129, 7321, 7417, 7687, 8089, 8161, 8431, 9127, 9241, 9337, 9511, 9631, 9871, 10009
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192574, A192580, A192597.

Programs

  • Mathematica
    start = {1}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, 3 x + 4 y], 3 x + 4 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]}]]]], # < 20000 &]];
t = FixedPoint[b, start]    (* A192596 *)
PrimePi[t]   (* A192597 *)

A192597 Index-list of the primes generated at A192596.

Original entry on oeis.org

0, 4, 11, 25, 31, 80, 110, 136, 202, 260, 282, 306, 344, 440, 449, 483, 508, 516, 547, 575, 669, 724, 730, 775, 793, 802, 854, 894, 907, 914, 933, 941, 975, 1017, 1024, 1055, 1131, 1146, 1155, 1178, 1190, 1218, 1231, 1266, 1274, 1338, 1348, 1392, 1420
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Examples

			From A192596=(1,7,31,97,127,...), the initial 1 is represented in A192597 by 0, followed by 4 since p(4)=7, followed by 11 since p(11)=31, etc.

Crossrefs

Cf. A192476, A192580, A192596.

Programs

A192614 Monotonic ordering of set S generated by these rules: if x and y are in S and 2x+y^2 is a prime, then 2x+y^2 is in S, and 1 is in S.

Original entry on oeis.org

1, 3, 7, 11, 23, 31, 47, 71, 103, 127, 151, 167, 191, 263, 311, 383, 431, 503, 631, 647, 743, 863, 887, 911, 967, 983, 1103, 1151, 1303, 1487, 1583, 1607, 1783, 1823, 1831, 1847, 1871, 2087, 2207, 2311, 2351, 2423, 2447, 2543, 2591, 2687, 2927, 3023
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2011

Keywords

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192476, A192580, A192615.

Programs

  • Mathematica
    start = {1}; primes = Table[Prime[n], {n, 1, 1000}];
f[x_, y_] := If[MemberQ[primes, 2 x + y^2], 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,
         Length[w]}]]]], # < 4000 &]];
t = FixedPoint[b, start]  (* A192614 *)
PrimePi[t]   (* A192615 *)

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 *)
Previous Showing 11-20 of 22 results. Next

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