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
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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
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Select[Range[2*10^4], PrimeQ[#] && Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 7 &] (* 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
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
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
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
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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
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Select[Prime[Range[5000]],Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 11&] (* 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
Period length in definition corrected, 103 added, 607 and 2063 removed. -
R. J. Mathar, Nov 08 2008
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
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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
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
-
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
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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
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
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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 *)
A333640
Numbers k such that the continued fraction of (1 + sqrt(k))/2 has period 13.
Original entry on oeis.org
421, 757, 1021, 1097, 1117, 1241, 1301, 1553, 1625, 1649, 1973, 2069, 2125, 2237, 2249, 2273, 2665, 2789, 2861, 3085, 3349, 3373, 3461, 3517, 3545, 3877, 3917, 4133, 4397, 4481, 4573, 4589, 4885, 5389, 5521, 5573, 5713, 5717, 6185, 6221, 6317, 6637, 6997, 7093
Offset: 1
a(1) = 421 because the continued fraction of (1 + sqrt(421))/2 = 10, 1, 3, 6, 1, 1, 2, 2, 1, 1, 6, 3, 1, 19, 1, 3, 6, ... has a period (1, 3, 6, 1, 1, 2, 2, 1, 1, 6, 3, 1, 19) of length 13.
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