A155560 Intersection of A000404 and A092572: N = a^2 + b^2 = c^2 + 3d^2 with a,b,c,d>0

13, 37, 52, 61, 73, 97, 100, 109, 117, 148, 157, 169, 181, 193, 208, 229, 241, 244, 277, 292, 313, 325, 333, 337, 349, 373, 388, 397, 400, 409, 421, 433, 436, 457, 468, 481, 541, 549, 577, 592, 601, 613, 628, 637, 657, 661, 673, 676, 709, 724, 733, 757, 769

Offset

1,1

Comments

Nonsquare terms of A155563. - Joerg Arndt, Jan 11 2015

Links

Table of n, a(n) for n=1..53.

Example

a(1)=13 is the least number that can be written as A+B and C+3D where A,B,C,D are positive squares (namely 13 = 2^2 + 3^2 = 1^2 + 3*2^2).
a(2)=37 is the second smallest number which figures in A000404 and in A092572 as well.

Prog

(PARI) isA155560(n /* omit optional 2nd arg for the present sequence */, c=[3, 1]) = { for(i=1, #c, for(b=1, sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2)&next(2)); return); 1}
for( n=1, 10^3, isA155560(n) & print1(n", "))
(PARI) is(n)=!issquare(n) && #bnfisintnorm(bnfinit(z^2+z+1), n) && #bnfisintnorm(bnfinit(z^2+1), n);
select(n->is(n), vector(1500, j, j)) \\ Joerg Arndt, Jan 11 2015

Crossrefs

Sequence in context: A119705 A343895 A343894 * A353198 A217734 A319969

Adjacent sequences: A155557 A155558 A155559 * A155561 A155562 A155563

Keyword

nonn

Author

M. F. Hasler, Jan 24 2009

Status

approved