A229769 Not of the form x^2 + P*y^2 for integers x > 0, y > 1, P a prime.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 18, 20, 23, 25, 26, 30, 35, 38, 39, 40, 42, 47, 50, 55, 58, 62, 65, 71, 74, 78, 83, 87, 90, 95, 98, 106, 110, 119, 122, 130, 138, 143, 146, 155, 158, 159, 167, 170, 182, 186, 190, 195, 203, 210, 215, 218, 222, 227, 230, 231, 250

Offset

1,2

Comments

There are no terms <= 10^9 greater than a(3036) = 69808035, leading to the conjecture that the sequence is finite. If true, every sufficiently large number is expressible as x^2 + P*y^2 with x > 0, y > 1.

Links

Chris Boyd, Table of n, a(n) for n = 1..3036

Example

Since 17 can be expressed as 3^2 + 2 * 2^2, it is not in the sequence.
No such expression exists for 18, hence it is in the sequence.
Since 19 can be expressed as 1^2 + 2 * 3^2, it is not in the sequence.

Prog

(PARI) test(n)={local(z, x, p, y); for(x=1, sqrtint(n), z=n-x^2; p=core(z); y=core(z, 1)[2]; if(isprime(p)&&y>1, return(1))); }
for(n=1, 300, if(test(n)==0, print1(n", ")))

Crossrefs

Supersequence of A074885 (x^2 + M*y^2, x > 0, y > 1, M > 0).

Supersequence of A212709 (not of the form p*c^2 + b^2, with p prime and c and b nonzero integers).

Sequence in context: A334142 A044919 A011871 * A130676 A039227 A257727

Adjacent sequences: A229766 A229767 A229768 * A229770 A229771 A229772

Keyword

nonn

Author

Chris Boyd, Sep 29 2013

Status

approved