A292313 Numbers that are the sum of three squares in arithmetic progression.

75, 300, 507, 675, 867, 1200, 1875, 2028, 2523, 2700, 3468, 3675, 4107, 4563, 4800, 5043, 6075, 7500, 7803, 8112, 8427, 9075, 10092, 10800, 11163, 12675, 13872, 14700, 15987, 16428, 16875, 18252, 19200, 20172, 21675, 22707, 23763, 24300, 24843, 27075, 28227, 30000, 30603

Offset: 1

Author

Antonio Roldán, Sep 14 2017

Keywords

• nonn

Examples

			75 = 1^2 + 5^2 + 7^2 = 1 + 25 + 49, with 25 - 1 = 49 - 25 = 24.
675 = 3^2 + 15^2 + 21^2 = 9 + 225 + 441, with 225 - 9 = 441 - 225 = 216.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A033428.

Cf. A000290, A000378, A004431, A134422, A292309, A292310, A292314, A292316.

Programs

PARI

t=4; k=3; while(t<=13000, i=k; e=0; v=t+i; while(i>1&&e==0, if(issquare(v), m=3*t; e=1; print1(m,", ")); i+=-2; v+=i); k+=2; t+=k)

Formula

Sequence is 3*(distinct elements in A198385).

Numbers of the form 3*m^2 where 2*m^2 is in A004431. - Chai Wah Wu, Oct 05 2017