A225835 Smallest prime p such that there is a prime q satisfying (2*n + 1)*p^2 - (2*n-1)*q^2 = 2, or 0 if no such p exists.

3, 26839, 11, 239, 379

Offset

1,1

Comments

Smallest prime p such that there is a prime q satisfying n*p^2 - (n-1)*q^2 = 1, or 0 if no such p exists: 5, 89,...

Primes p such that there is a prime q satisfying 5*p^2 - 3*q^2 = 2: 26839, 6391493137, 2540081 3820758542 5442608775 1898667220 6441480372 8945619713, ...

Primes q such that there is a prime p satisfying 5*p^2 - 3*q^2 = 2: 34649, 8251382159, 32792309 6359710073 4829167292 2880944251 7973351812 0308284159, ...

a(8) = 22656451 0158169057 8396614544 8202266647 1482614443 0220423848 3659973753 8209021958 1071702657 4442008471 0041419367 4411846431 - Giovanni Resta, May 16 2013

Conjecture: a(6) = a(7) = 0. Charles R Greathouse IV reports that a(6) must have thousands of digits. - Michael B. Porter, May 19 2013

Links

Table of n, a(n) for n=1..5.

Eric Weisstein's World of Mathematics, Pell Equation

Example

(2*2+1)*26839^2 - (2*2-1)*34649^2 = 3601659605 - 3601659603 = 2 and 26839, 34649 are primes, so a(2) = 26839.

Crossrefs

Cf. A033313, A225431.

Sequence in context: A171364 A307670 A115475 * A007350 A003839 A297023

Adjacent sequences: A225832 A225833 A225834 * A225836 A225837 A225838

Keyword

nonn

Author

Irina Gerasimova, May 16 2013

Extensions

a(2) from Giovanni Resta, May 15 2013

Status

approved