Christine Patterson has authored 25 sequences. Here are the ten most recent ones:
A341087
Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 6.
Original entry on oeis.org
3, 19, 43, 67, 139, 211, 571, 691, 883, 1483, 2011, 2539, 2851, 3331, 3931, 5779, 8011, 8779, 9811, 10459, 11131, 17851, 18379, 33331, 34819, 38299, 42571, 56659, 62731, 65179, 79699, 90931, 91939, 93811, 95419, 102859, 130579, 138139, 170179, 196771, 204019, 223939, 234259, 254731, 285139
Offset: 1
For D=139, the least x for which x^2 - D*y^2 = 6 has a solution is 59. The next prime, D, for which x^2 - D*y^2 = 6 has a solution is 163, but the smallest x in this case is 13, which is less than 59. The next prime, D, after 163 for which x^2 - D*y^2 = 6 has a solution is 211 and the least x for which it has a solution is 27265, which is larger than 59, so it is a new record value. So 139 is a term of this sequence and 59 is the corresponding term of A341088, but 163 is not a term here because the least x for which x^2 - D*y^2 = 6 has a solution is not a record value.
From _Jon E. Schoenfield_, Feb 20 2021: (Start)
As D runs through the primes, the minimal x values satisfying the equation x^2 - D*y^2 = 6 begin as follows (with primes D for which there are no solutions omitted):
.
x values satisfying minimal
D x^2 - D*y^2 = 6 x value record
-- -------------------- ------- ------
3 3, 9, 33, 123, ... 3 *
19 5, 109, 1591, ... 5 *
43 7, 1541, 47207, ... 7 *
67 41, 3577, ... 41 *
139 59, 3945595, ... 59 *
163 13, 14921333, ... 13
211 27265, 30627659, ... 27265 *
...
The record high minimal values of x (marked with asterisks) are the terms of A341088. The corresponding values of D are the terms of this sequence. (End)
A341086
Incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -5, where D is a prime number.
Original entry on oeis.org
1, 3, 21, 101661, 7661007, 4799633969721, 77198907060727563, 925844015429395821936018843, 42098324998788084039841633029, 11083764383781783138639570812583, 1490226373435897063030119543467763
Offset: 1
For D=29, the least positive y for which x^2 - D*y^2 = -5 has a solution is 3. The next prime, D, for which x^2 - D*y^2 = -5 has a solution is 41, but the smallest positive y in this case is 1, which is less than the previous record y, 3. So, 41 is not a term.
The next prime, D, after 41 for which x^2 - D*y^2 = -5 has a solution is 61 and the least positive y for which it has a solution is y=21, which is larger than 3, so it is a new record y value. So 61 is a term of A341085 and 21 is a term of this sequence.
A341085
Value of prime number D for incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -5.
Original entry on oeis.org
5, 29, 61, 109, 181, 661, 1021, 1549, 2161, 2389, 3169, 3469, 4909, 5581, 8929, 9601, 9949, 12841, 13381, 14029, 17029, 21169, 24709, 25309, 28729, 31249, 32869, 34549, 35149, 39901, 40429, 43801, 48049, 49009, 56401, 56701, 62701, 63541, 70141, 86269
Offset: 1
For D=29, the least positive y for which x^2 - D*y^2 = -5 has a solution is 3. The next prime, D, for which x^2 - D*y^2 = -5 has a solution is 41, but the smallest positive y in this case is 1, which is less than the previous record y, 3. So, 41 is not a term.
The next prime, D, after 41 for which x^2 - D*y^2 = -5 has a solution is 61 and the least positive y for which it has a solution is y=21, which is larger than 3, so it is a new record y value. So 61 is a term of this sequence and 21 is the corresponding term of A341086.
From _Jon E. Schoenfield_, Feb 20 2021: (Start)
As D runs through the primes, the minimal y values satisfying the equation x^2 - D*y^2 = -5 begin as follows:
.
y values satisfying minimal
D x^2 - D*y^2 = -5 y value record
-- -------------------- ------- ------
2 (none)
3 (none)
5 1, 9, 161, 2889, ... 1 *
7 (none)
11 (none)
13 (none)
17 (none)
19 (none)
23 (none)
29 3, 283, 58523, ... 3 *
31 (none)
37 (none)
41 1, 129, 3969, ... 1
43 (none)
47 (none)
51 (none)
53 (none)
59 (none)
61 21, 3447309, ... 21 *
...
The record high minimal values of y (marked with asterisks) are the terms of A341086. The corresponding values of D are the terms of this sequence. (End)
A341084
Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -5, where D is a prime number.
Original entry on oeis.org
0, 16, 164, 1061372, 103068308, 162122886, 123398206659664, 2466743672871107188, 36438755210133838109283894464, 1957006192940494702014893262914, 541745559127518723115014358590896, 83890612389598737813497437560727166
Offset: 1
For D=29, the least x for which x^2 - D*y^2 = -5 has a solution is 16. The next prime, D, for which x^2 - D*y^2 = -5 has a solution is 41, but the smallest x in this case is 6, which is less than 16. The next prime, D, after 41 for which x^2 - D*y^2 = -5 has a solution is 61 and the least x for which it has a solution is 164, which is larger than 16, so it is a new record value. 29 is a term of A341083 and 16 is a term of this sequence, but 41 is not a term of A341083 because the least x for which x^2 - D*y^2 = -5 has a solution is not a record value.
A341083
Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -5.
Original entry on oeis.org
5, 29, 61, 109, 181, 641, 661, 1021, 1549, 2161, 2389, 3169, 3469, 4909, 5581, 8929, 9601, 9949, 12841, 13381, 14029, 17029, 21169, 24709, 25309, 28729, 31249, 32869, 34549, 35149, 39901, 40429, 43801, 48049, 49009, 56401, 56701, 62701, 63541, 70141, 86269, 91009
Offset: 1
For D=29, the least x for which x^2 - D*y^2 = -5 has a solution is 16. The next prime, D, for which x^2 - D*y^2 = -5 has a solution is 41, but the smallest x in this case is 6, which is less than 16. The next prime, D, after 41 for which x^2 - D*y^2 = -5 has a solution is 61 and the least x for which it has a solution is 164, which is larger than 16, so it is a new record value. So 29 is a term of this sequence and 16 is the corresponding term of A341084, but 41 is not a term here because the least x for which x^2 - D*y^2 = -5 has a solution is not a record value.
From _Jon E. Schoenfield_, Feb 20 2021: (Start)
As D runs through the primes, the minimal x values satisfying the equation x^2 - D*y^2 = -5 begin as follows:
.
x values satisfying minimal
D x^2 - D*y^2 = -5 x value record
-- --------------------- ------- ------
2 (none)
3 (none)
5 0, 20, 360, 6460, ... 0 *
7 (none)
11 (none)
13 (none)
17 (none)
19 (none)
23 (none)
29 16, 1524, 315156, ... 16 *
31 (none)
37 (none)
41 6, 826, 25414, ... 6
43 (none)
47 (none)
51 (none)
53 (none)
59 (none)
61 164, 26924344, ... 164 *
...
The record high minimal values of x (marked with asterisks) are the terms of A341084. The corresponding values of D are the terms of this sequence. (End)
A341082
Incrementally largest values of minimal y satisfying the equation x^2-D*y^2=5, where D is a prime number.
Original entry on oeis.org
2, 58, 1922, 35078, 76016042, 1161958198, 233025369988282, 5732081667022982, 6162672978871449862, 4778628197827994122556402, 3995105338251652225860073210642, 9319999956851141533879334192705803394284705042
Offset: 1
For D=19, the least positive y for which x^2-D*y^2=5 has a solution is 2. The next prime, D, for which x^2-D*y^2=5 has a solution is 29, but the smallest positive y in this case is 2, which is equal to the previous record y. So, 29 is not a term.
The next prime, D, after 19 for which x^2-D*y^2=5 has a solution is 61 and the least positive y for which it has a solution is y=58, which is larger than 2, so it is a new record y value. So 61 is a term of A341081 and 58 is a term of this sequence.
A341081
Value of prime number D for incrementally largest values of minimal y satisfying the equation x^2-D*y^2=5.
Original entry on oeis.org
19, 61, 149, 241, 409, 421, 541, 1069, 1249, 1381, 1621, 4261, 4621, 4789, 6301, 8269, 12601, 12721, 14449, 16069, 20101, 32029, 33889, 34381, 35281, 38329, 43261, 45061, 60589, 87481, 89989, 97549, 99661, 121081, 125101, 166021, 178621, 187069, 191689, 202381
Offset: 1
For D=19, the least positive y for which x^2-D*y^2=5 has a solution is 2. The next prime, D, for which x^2-D*y^2=5 has a solution is 29, but the smallest positive y in this case is 2, which is equal to the previous record y. So, 29 is not a term.
The next prime, D, after 19 for which x^2-D*y^2=5 has a solution is 61 and the least positive y for which it has a solution is y=58, which is larger than 2, so it is a new record y value. So 61 is in this sequence and 58 is in A341082.
A341078
Incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -3, where D is a prime number.
Original entry on oeis.org
1, 2, 722, 837158, 77228318, 5436980738, 49637737974482, 462761120757722506058, 2836540596515452087502, 37216095020093890760397134162, 1858485134141860820807351059562927114738, 42507485681147639763501995374671391449914
Offset: 1
From _Jon E. Schoenfield_, Feb 23 2021: (Start)
As D runs through the primes, the minimal y values satisfying the equation x^2 - D*y^2 = -3 begin as follows:
.
x values satisfying minimal
D x^2 - D*y^2 = -5 y value record
-- ---------------------- ------- ------
2 (none)
3 1, 2, 7, 26, 97, ... 1 *
5 (none)
7 1, 2, 14, 31, 223, ... 1
11 (none)
13 2, 38, 2558, ... 2 *
17 (none)
19 1, 14, 326, 4759, ... 1
23 (none)
29 (none)
31 2, 37, 604, ... 2
37 (none)
41 (none)
43 2, 61, 13867, ... 2
47 (none)
53 (none)
59 (none)
61 722, 60158, ... 722 *
...
The record high minimal values of y (marked with asterisks) are the terms of this sequence. The corresponding values of D are the terms of A341077. (End)
A341077
Value of prime number D for incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -3.
Original entry on oeis.org
3, 13, 61, 181, 397, 541, 661, 1021, 1381, 1621, 3361, 3529, 4201, 4261, 4621, 6421, 9241, 9601, 9949, 12541, 20161, 23209, 25309, 32869, 37321, 43261, 71821, 78901, 82021, 112429, 127261, 131041, 137089, 139309, 144169, 169789, 183661, 226669, 300301
Offset: 1
For D=13, the least positive y for which x^2 - D*y^2 = -3 has a solution is 2. The next primes, D, for which x^2 - D*y^2 = -3 has a solution are 19, 31, and 43, but the smallest positive y in each of those cases is 1 or 2, neither of which is larger than the previous record y, 2. So 19, 31, and 43 are not terms of this sequence.
The next prime, D, after 43 for which x^2 - D*y^2 = -3 has a solution is 61, and the least positive y for which it has a solution is y=722, which is larger than 2, so it is a new record y value. So 61 is a term of this sequence and 722 is the corresponding term of A341078.
A336800
Incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = 3, where D is a prime number.
Original entry on oeis.org
1, 11, 913, 23111, 221161, 3450467, 78495388880651, 10727569485920362724490720830137, 2027623752997677729366859925491727716361771, 127194478138610620242010764302143341359067289, 264781463133512691674640873276575271478272395041
Offset: 1
For D=13, the least positive y for which x^2-D*y^2=3 has a solution is 1. The next prime, D, for which x^2-D*y^2=3 has a solution is 61, but the smallest positive y in this case is also 1, which is equal to the previous record y. So, 61 is not a term.
The next prime, D, after 13 for which x^2-D*y^2=3 has a solution is 73 and the least positive y for which it has a solution is y=11, which is larger than 1, so it is a new record y value. So, 73 is a term of A336796 and 11 is a term of this sequence.
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