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.

Showing 1-10 of 37 results. Next

A146360 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 15: primes in A146338.

Original entry on oeis.org

193, 281, 1861, 1933, 2089, 2141, 2437, 2741, 2837, 3037, 3121, 3413, 4001, 4637, 4877, 5821, 6653, 7673, 8117, 10069, 10273, 10457, 11197, 11549, 11821, 12409, 13037, 14653, 15061, 15077, 18661, 20549, 22921, 23117, 24169, 25621, 28837, 35597, 35869, 36389, 38569
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: isA146360 := proc(n) RETURN(isprime(n) and A146326(n) = 15) ; end: for n from 2 to 30000 do if isA146360(n) then printf("%d,\n",n) ; fi; od: # R. J. Mathar, Sep 06 2009
  • Mathematica
    Select[Prime[Range[1500]],Length[ContinuedFraction[(Sqrt[#]+1)/2][[2]]] == 15&] (* Harvey P. Dale, Aug 16 2014 *)

Extensions

8539 removed by R. J. Mathar, Sep 06 2009
More terms from Amiram Eldar, Mar 30 2020

A050969 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 20.

Original entry on oeis.org

151, 199, 367, 622, 863, 1151, 1454, 1501, 1502, 1941, 2033, 3902, 4101, 4317, 4677, 4821, 5549, 6077, 7277, 8133, 8453, 8813, 9253, 9357, 11381, 11733, 14237, 15837, 17933, 18293, 21653, 23453, 25157, 36077, 49013
Offset: 1

Views

Author

N. J. A. Sloane, Jan 04 2000

Keywords

References

  • R. A. Mollin, Quadratics, CRC Press, 1996, Appendix A.

Links

Crossrefs

Cf. A050950-A050969, A051962-A051965.

A051962 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 21.

Original entry on oeis.org

337, 569, 977, 1453, 1669, 1741, 2053, 2293, 4093, 4349, 5437, 5557, 8861, 9341, 10133, 10709, 11117, 12917, 14549, 15053, 16253, 18413, 18917, 19013, 19973, 20117, 20333, 25373, 28493, 29333
Offset: 1

Views

Author

N. J. A. Sloane, Jan 04 2000

Keywords

References

  • R. A. Mollin, Quadratics, CRC Press, 1996, Appendix A.

Crossrefs

Cf. A050950-A050969, A051962-A051965.

A051965 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 24.

Original entry on oeis.org

271, 382, 607, 753, 911, 1103, 1262, 1438, 1473, 1838, 1982, 2063, 2078, 2558, 2661, 2687, 2893, 2903, 3986, 3113, 3167, 3377, 3669, 4237, 4333, 4533, 5293, 5533, 5753, 6509, 6621, 7197, 7269, 8153, 8189, 8213, 8413, 10637, 11157, 11573, 11589, 11893, 12677, 12797, 13453, 13541, 14117, 15693, 15917, 17133, 17309, 18677, 18933, 19797, 20053, 20373, 20837, 22757, 25709, 25973, 26213, 27317, 34997, 39077
Offset: 1

Views

Author

N. J. A. Sloane, Jan 04 2000

Keywords

References

  • R. A. Mollin, Quadratics, CRC Press, 1996, Appendix A.

Links

Crossrefs

Cf. A050950-A050969, A051962-A051965.

Extensions

a(40) and following from Georg Fischer, Sep 20 2021

A146362 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 17 : primes in A146340.

Original entry on oeis.org

521, 617, 709, 1433, 1597, 2549, 2909, 3581, 3821, 4013, 4649, 5501, 5693, 5813, 6197, 7853, 8093, 8573, 9281, 9677, 10597, 10973, 11273, 13109, 13613, 15413, 15641, 15737, 16001, 16477, 17093, 20261, 22637, 24697, 26717, 32413, 35537, 38177, 43717, 46649, 47681
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]]] == 17 &] (* Amiram Eldar, Mar 30 2020 *)

Extensions

Period length in definition corrected, 2579, 5003 removed, 5813 inserted by R. J. Mathar, Sep 06 2009
More terms from Amiram Eldar, Mar 30 2020

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
Showing 1-10 of 37 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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