A255232 - OEIS

A255232

One half of the fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = -A007522(n), n >= 1 (primes congruent to 7 mod 8).

1, 2, 2, 3, 3, 4, 4, 4, 5, 6, 5, 5, 7, 6, 6, 7, 7, 9, 7, 7, 8, 10, 8, 9, 8, 8, 9, 11, 10, 9, 10, 13, 11, 10, 13, 14, 12, 11, 13, 11, 11, 12, 13, 12, 14, 13, 16, 12, 12, 17, 13, 14, 13, 16, 13, 18, 14, 16, 15, 14, 17, 14, 15, 14, 14, 14, 17, 16, 19, 16, 17, 16, 20

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OFFSET

1,2

COMMENTS

For the corresponding term x1(n) see A254938(n).

See A254938 also for the Nagell reference.

The least positive y solutions (that is those of the first class) for the primes +1 and -1 (mod 8) together (including prime 2) are given in A255246.

LINKS

Table of n, a(n) for n=1..73.

FORMULA

A254938(n)^2 - 2*(2*a(n))^2 = -A007522(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.

EXAMPLE