A050969 -id:A050969 - cp's OEIS frontend

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

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

Artur Jasinski, Oct 30 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..1000

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

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

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

Artur Jasinski, Oct 30 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..2000

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

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 *)

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

Artur Jasinski, Oct 30 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..1000

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

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

Select[Range[2*10^4], PrimeQ[#] && Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 14 &] (* Amiram Eldar, Mar 30 2020 *)

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

Artur Jasinski, Oct 30 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..1000

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

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 *)

3391 removed - R. J. Mathar, Sep 06 2009

More terms from Amiram Eldar, Mar 30 2020

A050960 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 11.

Original entry on oeis.org

541, 593, 661, 701, 857, 1061, 1109, 1217, 1237, 1709, 1733, 1949, 2333, 2957, 3677, 3701, 4373, 5237, 5309, 7013, 8693, 9533, 10853, 12437

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

R. A. Mollin and H. C. Williams, On a determination of real quadratic fields of class number one and related continued fraction period length less than 25, Proc. Japan Acad. Ser. A Math. Sci. Volume 67, Number 1 (1991), 20-25. (cf. Table 3.1)

Cf. A050950-A050969, A051962-A051965.

A050952 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 3.

Original entry on oeis.org

17, 37, 61, 101, 197, 317, 461, 557, 677, 773, 1877

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

R. A. Mollin and H. C. Williams, On a determination of real quadratic fields of class number one and related continued fraction period length less than 25, Proc. Japan Acad. Ser. A Math. Sci. Volume 67, Number 1 (1991), 20-25. (cf. Table 3.1)

Cf. A050950-A050969, A051962-A051965.

A050954 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 5.

Original entry on oeis.org

41, 149, 157, 181, 269, 397, 941, 1013, 2477, 2693, 3533, 4253

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

R. A. Mollin and H. C. Williams, On a determination of real quadratic fields of class number one and related continued fraction period length less than 25, Proc. Japan Acad. Ser. A Math. Sci. Volume 67, Number 1 (1991), 20-25. (cf. Table 3.1)

Cf. A050950-A050969, A051962-A051965.

A050951 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 2.

Original entry on oeis.org

3, 6, 11, 21, 38, 77, 83, 93, 227, 237, 437, 453, 1133, 1253

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

R. A. Mollin and H. C. Williams, On a determination of real quadratic fields of class number one and related continued fraction period length less than 25, Proc. Japan Acad. Ser. A Math. Sci. Volume 67, Number 1 (1991), 20-25. (cf. Table 3.1)

Cf. A050950-A050969, A051962-A051965.

A050953 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 4.

Original entry on oeis.org

7, 14, 23, 33, 47, 62, 69, 133, 141, 167, 213, 398, 413, 573, 717, 1077, 1293, 1397, 1757, 3053

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

R. A. Mollin and H. C. Williams, On a determination of real quadratic fields of class number one and related continued fraction period length less than 25, Proc. Japan Acad. Ser. A Math. Sci. Volume 67, Number 1 (1991), 20-25. (cf. Table 3.1)

Cf. A050950-A050969, A051962-A051965.

A050955 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 6.

Original entry on oeis.org

19, 22, 57, 59, 107, 131, 253, 278, 309, 341, 381, 749, 813, 893, 1893, 2453, 2757, 3317

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

R. A. Mollin and H. C. Williams, On a determination of real quadratic fields of class number one and related continued fraction period length less than 25, Proc. Japan Acad. Ser. A Math. Sci. Volume 67, Number 1 (1991), 20-25. (cf. Table 3.1)

Cf. A050950-A050969, A051962-A051965.

cp's OEIS Frontend

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

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

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

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

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A050960 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 11.

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A050952 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 3.

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A050954 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 5.

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A050951 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 2.

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A050953 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 4.

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A050955 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 6.

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