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URL: https://oeis.org/A254935

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A254935
Fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = -A007519(n), n>=1 (primes congruent to 1 mod 8).
7
3, 5, 7, 7, 7, 9, 9, 11, 11, 11, 13, 15, 13, 13, 17, 15, 17, 19, 15, 17, 21, 17, 17, 21, 19, 23, 19, 19, 21, 23, 25, 21, 21, 27, 23, 29, 23, 23, 23, 23, 27, 25, 29, 31, 25, 33, 25, 27, 31, 29, 35, 27, 27, 31, 35, 33, 29, 35, 29, 31, 35, 31, 37, 31, 31, 33, 31, 41, 43, 39, 35, 37, 33, 41, 33, 35, 41
OFFSET
1,1
COMMENTS
For the corresponding term x1(n) see A254934(n).
See A254934 also for the Nagell reference.
The least positive y solutions (that is the ones of the first class) for the primes +1 and -1 (mod 8) together (including prime 2) are given in A255246.
LINKS
M. F. Hasler, Table of n, a(n) for n = 1..1000, May 22 2025
FORMULA
A254934(n)^2 - 2*a(n)^2 = -A007519(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.
EXAMPLE
See A254934.
n = 3: 5^2 - 2*7^2 = 25 - 98 = -73.
PROG
(PARI) apply( {A254935(n, p=A007519(n))=sqrtint((A254934(, p)^2+p)\2)}, [1..77]) \\ M. F. Hasler, May 22 2025
CROSSREFS
Cf. A007519 (primes == 1 mod 8), A005123 (8k+1 is prime).
Cf. A254934 (corresponding x1 values), A254936 (x2 values), A254937 (y2 values), A254938 (same for primes == 7 mod 8), A255232 (y2 values, halved).
Sequence in context: A297346 A342622 A211517 * A376760 A104199 A103470
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 18 2015
EXTENSIONS
More terms from M. F. Hasler, May 22 2025
STATUS
approved