

A164986


Numbers of the form 2p^2 = q^2 + 1, where p and q are primes.


0




OFFSET

1,1


COMMENTS

A079704 INTERSECT A002522. Subsequence of A088920 (Solutions k to the Diophantine equation k = 2n^2 = m^2+1): those terms for which associated m in A002315 and n in A001653 are both prime.
Corresponding p are prime Pell numbers (prime denominators of continued fraction convergents to sqrt(2)).
Corresponding q are prime numerators of the continued fraction convergents to sqrt(2).
Corresponding p, q, p^2, q^2, (p,q), (q,p), etc., form subsequences of many other OEIS sequences; see crossreferences.
Any further terms are too large to include here.


LINKS

Table of n, a(n) for n=1..4.


FORMULA

a(n) = 2*(A118612(n+1))^2 = (A086397(n+1))^2 + 1.


EXAMPLE

a(1) = 50 as 50 = 2*5^2 = 7^2 + 1, where 5 and 7 are prime.


CROSSREFS

Cf. A088920, A118612, A086397, A086395, A002315 (NSW numbers), A088165 (prime NSW numbers = prime RMS numbers (A140480)), A001653, A000129 (Pell numbers), A086383, A101411, A079704, A002522, A008843, A104683, A163742, etc.
Sequence in context: A075912 A062151 A001241 * A224121 A238283 A240191
Adjacent sequences: A164983 A164984 A164985 * A164987 A164988 A164989


KEYWORD

nonn


AUTHOR

Rick L. Shepherd, Sep 03 2009


STATUS

approved



