The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A341079

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A341079

Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 5.
(history; published version)

#12 by N. J. A. Sloane at Sat Feb 27 21:50:41 EST 2021

STATUS

proposed

approved

#11 by Jon E. Schoenfield at Tue Feb 23 22:42:24 EST 2021

STATUS

editing

proposed

#10 by Jon E. Schoenfield at Tue Feb 23 22:42:09 EST 2021

DATA

5, 19, 29, 41, 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

COMMENTS

Analogous to A033316 for x^2 - D*y^2 = 1, and D is required to be prime, and for record values of x.

EXAMPLE

For D=29, the least x for which x^2 - D*y^2 = 5 has a solution is 11. The next prime, D, for which x^2 - D*y^2 = 5 has a solution is 31, but the smallest x in this case is 6, which is less than 11. The next prime, D, after 31 for which x^2 - D*y^2 = 5 has a solution is 41 and the least x for which it has a solution is 13, which is larger than 11, so it is a new record value. 29 is a term for of this sequence and 11 is a the corresponding term of A341080, but 31 is not a term of this sequence because at D=31 the least x for which x^2 - D*y^2 = 5 has a solution is not a record value.

EXTENSIONS

a(1)=5 inserted and Example section edited by Jon E. Schoenfield, Feb 23 2021

#9 by N. J. A. Sloane at Sun Feb 14 13:11:11 EST 2021

STATUS

proposed

editing

Discussion

Sun Feb 21

13:45

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A341079 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#8 by Jon E. Schoenfield at Sat Feb 13 22:08:01 EST 2021

STATUS

editing

proposed

#7 by Jon E. Schoenfield at Sat Feb 13 22:06:56 EST 2021

NAME

Value of prime number D for incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 5.

EXAMPLE

For D=29, the least x for which x^2-D*y^2=5 has a solution is 11. The next prime, D, for which x^2-D*y^2=5 has a solution is 31, but the smallest x in this case is 6, which is less than 11. The next prime, D, after 31 for which x^2-D*y^2=5 has a solution is 41 and the least x for which it has a solution is 13, which is larger than 11, so it is a new record value. 29 is a term for this sequence and 11 qualifies for membership to is a term of A341080, but 31 does is not qualify because the least x for which x^2-D*y^2=5 has a solution is not a record value.

STATUS

approved

editing

Discussion

Sat Feb 13

22:08

Jon E. Schoenfield: Why is D=5 missing from the Data here?  (Please see A341080.)

#6 by N. J. A. Sloane at Sat Feb 13 14:56:23 EST 2021

STATUS

proposed

approved

#5 by Christine Patterson at Mon Feb 08 14:56:55 EST 2021

STATUS

editing

proposed

#4 by Christine Patterson at Mon Feb 08 14:56:24 EST 2021

EXAMPLE

For D=29, the least x for which x^2-D*y^2=5 has a solution is 11. The next prime, D, for which x^2-D*y^2=5 has a solution is 31, but the smallest x in this case is 6, which is less than 3111. The next prime, D, after 31 for which x^2-D*y^2=5 has a solution is 41 and the least x for which it has a solution is 13, which is larger than 31, 11, so it is a new record value. 29 is a term for this sequence and 11 qualifies for membership to A341080, but 31 does not qualify because the least x for which x^2-D*y^2=5 has a solution is not a record value.

STATUS

proposed

editing

#3 by Christine Patterson at Thu Feb 04 20:33:54 EST 2021

STATUS

editing

proposed

Discussion

Thu Feb 04

21:02

Jon E. Schoenfield: "13, which is larger than 31"?