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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A146351 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 6: primes in A146331.

Original entry on oeis.org

19, 59, 107, 131, 499, 659, 1627, 1907, 2251, 2467, 3803, 4139, 4283, 5827, 6779, 9539, 10067, 11491, 12619, 13763, 16987, 18587, 18803, 19507, 22003, 23003, 23819, 24859, 28643, 30859, 37507, 40939, 42083, 42299, 43403, 43867, 44563, 52747, 53507, 55339
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2008

Keywords

Links

Crossrefs

Cf. A000290, A078370, A146326-A146345, A146348-A146360.

Programs

  • Maple
    A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic','quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146351 := proc(n) RETURN(isprime(n) and A146326(n) = 6) ; end: for n from 2 to 13000 do if isA146351(n) then printf("%d,\n",n) ; fi; od: # R. J. Mathar, Sep 06 2009
  • Mathematica
    Select[Prime[Range[10000]],Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 6&] (* Harvey P. Dale, Dec 22 2013 *)

Extensions

797 removed by R. J. Mathar, Sep 06 2009
More terms from Harvey P. Dale, Dec 22 2013

A146352 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 7: primes in A146332.

Original entry on oeis.org

89, 109, 113, 137, 373, 389, 509, 653, 797, 853, 997, 1009, 1493, 1997, 2309, 2621, 2677, 3797, 4973, 7817, 7873, 9829, 9833, 12197, 12269, 12821, 14009, 15773, 16661, 16673, 18253, 18269, 20389, 21557, 24197, 24533, 25037, 25741, 30677, 31973, 33941, 34253, 35977
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2008

Keywords

Links

Crossrefs

Cf. A000290, A050950-A050969, A078370, A146326-A146345, A146348-A146360.

Programs

  • Maple
    A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic','quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146352 := proc(n) RETURN(isprime(n) and A146326(n) = 7) ; end: for n from 2 to 13000 do if isA146352(n) then printf("%d,\n",n) ; fi; od: # R. J. Mathar, Sep 06 2009
  • Mathematica
    Select[Range[2*10^4], PrimeQ[#] && Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 7 &] (* Amiram Eldar, Mar 30 2020 *)

Extensions

607 removed, 797 inserted by R. J. Mathar, Sep 06 2009
More terms from Amiram Eldar, Mar 30 2020

A146353 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 8; primes in A146333.

Original entry on oeis.org

31, 71, 383, 503, 743, 983, 1327, 2543, 4271, 5711, 6151, 8543, 9871, 14503, 17783, 21191, 22031, 25463, 35023, 35759, 36263, 36559, 40543, 46471, 47711, 60727, 66343, 72551, 73751, 75767, 81551, 83639, 91463, 98327, 142183, 159407, 160343, 193031, 195743, 218623
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2008

Keywords

Links

Crossrefs

Cf. A000290, A050950-A050969, A078370, A146326-A146345, A146348-A146360.

Programs

  • Mathematica
    Select[Prime[Range[10000]], 8 == Length[ContinuedFraction[(1 + Sqrt[#])/2][[2]]] &]

Extensions

8467 removed - R. J. Mathar, Sep 06 2009
Extended by T. D. Noe, Mar 22 2011
More terms from Amiram Eldar, Mar 30 2020

A146354 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 9: primes in A143577.

Original entry on oeis.org

73, 97, 233, 277, 349, 353, 613, 821, 877, 1181, 1277, 1613, 1637, 1693, 2357, 2777, 3557, 3989, 4157, 4517, 4889, 4933, 5261, 6113, 7213, 9133, 9181, 9749, 10313, 10909, 11057, 11213, 11257, 12161, 12301, 13033, 16217, 16741, 17989, 19469
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2008

Keywords

Links

Crossrefs

Cf. A000290, A050950-A050969, A078370, A146326-A146345, A146348-A146360.

Programs

  • Mathematica
    Select[Prime[Range[2300]],Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 9&] (* Harvey P. Dale, Aug 22 2011 *)

Extensions

A-number in definition corrected. 1613 and 4933 inserted, 9421 deleted, extended beyond 9749 by R. J. Mathar, Nov 09 2008

A146355 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 10 : primes in A146335.

Original entry on oeis.org

43, 67, 563, 827, 1787, 1811, 2099, 2459, 5107, 7643, 8363, 9323, 9371, 9467, 12251, 13499, 23539, 24251, 28411, 35059, 41843, 47563, 49531, 51419, 57731, 66851, 82787, 94547, 109267, 123499, 123923, 126443, 127643, 134363, 135467, 138587, 162251, 180419, 181019
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2008

Keywords

Links

Crossrefs

Cf. A000290, A050950-A050969, A078370, A146326-A146345, A146348-A146360.

Programs

  • Mathematica
    Select[Prime[Range[10000]],Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 10&] (* Harvey P. Dale, Jul 13 2019 *)

Extensions

More terms from Harvey P. Dale, Jul 13 2019
More terms from Amiram Eldar, Mar 30 2020

A146356 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 11: primes in A146335.

Original entry on oeis.org

541, 593, 661, 701, 857, 1061, 1109, 1217, 1237, 1709, 1733, 1949, 2333, 2557, 2957, 3229, 3677, 3701, 4373, 5081, 5237, 5309, 6133, 7013, 8693, 9533, 10333, 10853, 12437, 14197, 19213, 20693, 21101, 23173, 29753, 30949, 33797, 36677, 37781, 37993, 41813
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2008

Keywords

Links

Crossrefs

Cf. A000290, A050950-A050969, A078370, A146326-A146345, A146348-A146360.

Programs

  • Maple
    A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic','quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146356 := proc(n) RETURN(isprime(n) and A146326(n) = 11) ; end: for n from 2 to 30000 do if isA146356(n) then printf("%d,\n",n) ; fi; od: # R. J. Mathar, Sep 06 2009
  • Mathematica
    Select[Prime[Range[5000]],Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 11&] (* Harvey P. Dale, Apr 27 2016 *)

Extensions

1721 and 6491 removed by R. J. Mathar, Sep 06 2009
More terms from Harvey P. Dale, Apr 27 2016

A146357 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 12 : primes in A146336.

Original entry on oeis.org

103, 127, 239, 263, 479, 887, 1567, 2711, 5743, 5903, 8311, 8447, 10567, 10847, 12391, 14783, 14831, 15887, 18191, 22343, 23447, 28151, 31391, 32359, 40087, 40343, 42703, 53407, 60103, 60623, 64231, 75431, 79943, 81559, 83663, 93503, 114167, 130199, 135119, 141863
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2008

Keywords

Links

Crossrefs

Cf. A000290, A050950-A050969, A078370, A146326-A146345, A146348-A146360.

Programs

  • Mathematica
    Select[Prime[Range[10000]],Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 12&] (* Harvey P. Dale, May 18 2017 *)

Extensions

Period length in definition corrected, 103 added, 607 and 2063 removed. - R. J. Mathar, Nov 08 2008
More terms from Amiram Eldar, Mar 30 2020

A146358 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 13: primes in A333640.

Original entry on oeis.org

421, 757, 1021, 1097, 1117, 1301, 1553, 1973, 2069, 2237, 2273, 2789, 2861, 3373, 3461, 3517, 3877, 3917, 4133, 4397, 4481, 5521, 5573, 5717, 6221, 6317, 6637, 6997, 7253, 7517, 8741, 9049, 9173, 9437, 10181, 10949, 11597, 11789, 12497, 15473, 15797, 16141, 18353
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2008

Keywords

Links

Crossrefs

Cf. A000290, A050950-A050969, A078370, A146326-A146345, A333640, A146348-A146360.

Programs

  • Mathematica
    Select[Range[2*10^4], PrimeQ[#] && Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 13 &] (* Amiram Eldar, Mar 30 2020 *)
Select[Prime[Range[2500]],Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]]==13&] (* Harvey P. Dale, Mar 05 2023 *)

Extensions

Definition corrected, 3 terms added. - R. J. Mathar, Nov 08 2008
More terms from Amiram Eldar, Mar 30 2020

A146359 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 14: primes in A146337.

Original entry on oeis.org

179, 251, 307, 347, 467, 587, 683, 1987, 5099, 5683, 7883, 8059, 8707, 12227, 14867, 15083, 15227, 22283, 34883, 40627, 42787, 47819, 50147, 51683, 68147, 73547, 78467, 84523, 84979, 89051, 95219, 104947, 106451, 107699, 132707, 134291, 142811, 149939, 164051
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2008

Keywords

Links

Crossrefs

Cf. A000290, A050950-A050969, A078370, A146326-A146345, A146348-A146360.

Programs

  • Maple
    A := proc(n) local c; try c := numtheory[cfrac](1/2+sqrt(n)/2,'periodic,quotients') ; RETURN(nops(c[2]) ); catch: RETURN(-1) end try ; end: isA146337 := proc(n) if A(n) = 14 then RETURN(true); else RETURN(false); fi; end: isA146359 := proc(n) RETURN(isprime(n) and isA146337(n)) ; end: for k from 1 do if isA146359(ithprime(k)) then printf("%d, ",ithprime(k)) ; fi; od: # R. J. Mathar, Nov 08 2008
  • Mathematica
    Select[Range[2*10^4], PrimeQ[#] && Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 14 &] (* Amiram Eldar, Mar 30 2020 *)

Extensions

5813 and 6791 removed, extended beyond 8707 by R. J. Mathar, Nov 08 2008
More terms from Amiram Eldar, Mar 30 2020

A146361 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 16 : primes in A146339.

Original entry on oeis.org

191, 311, 431, 647, 1319, 1487, 2351, 5527, 9431, 19087, 21143, 24359, 27239, 29207, 32183, 34367, 36791, 38711, 41759, 42071, 43063, 43319, 49367, 58271, 58391, 59399, 62327, 65183, 66239, 77543, 82759, 84263, 87407, 90271, 93967, 94463, 97127, 100703, 101063
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2008

Keywords

Links

Crossrefs

Cf. A000290, A050950-A050969, A078370, A146326-A146345, A146348-A146360.

Programs

  • Mathematica
    Select[Range[2*10^4], PrimeQ[#] && Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 16 &] (* Amiram Eldar, Mar 30 2020 *)
Select[Prime[Range[10000]],Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]]==16&] (* Harvey P. Dale, Apr 12 2025 *)

Extensions

3391 removed - R. J. Mathar, Sep 06 2009
More terms from Amiram Eldar, Mar 30 2020
Previous Showing 21-30 of 36 results. Next

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