|
|
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 cross-references.
Any further terms are too large to include here.
|
|
LINKS
|
|
|
FORMULA
|
|
|
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.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|