A256074 Squares representable as k*m + k + m, where k >= m > 1 are squares.

49, 169, 324, 441, 961, 1849, 2209, 3249, 5329, 8281, 12321, 15129, 17424, 17689, 24649, 33489, 44521, 58081, 58564, 64009, 65025, 74529, 94249, 103684, 117649, 145161, 177241, 191844, 214369, 237169, 257049, 305809, 361201, 423801, 480249, 494209, 573049, 660969, 700569

Offset: 1

Author

Alex Ratushnyak, Mar 14 2015

Keywords

• nonn

Comments

A subsequence of A254671.

The sequence of square roots of a(n) begins: 7, 13, 18, 21, 31, 43, 47, 57, 73, 91, 111, 123, 132, 133, 157, 183, 211, 241, 242, 253, 255, 273, 307, 322, 343.

This sequence is infinite via x = m^2 and y = (m + 1)^2 so then x*y + x + y = m^2 * (m + 1)^2 + m^2 + (m + 1)^2 = m^4 + 2*m^3 + 3*m^2 + 2*m + 1 = (m^2 + m + 1)^2. - David A. Corneth, Oct 19 2024

Examples

			a(1) = 49 = 4*9 + 4 + 9.
a(2) = 169 = 9*16 + 9 + 16.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10657 (terms <= 10^16)

Crossrefs

Cf. A000290, A058031, A066938, A254671.

Programs

PARI

v=[];for(m=2,100,for(k=m,10^3,if(issquare(s=(k*m)^2+k^2+m^2),v=concat(v,s))));vecsort(v) \\ Derek Orr, Mar 21 2015

Extensions

More terms from David A. Corneth, Oct 19 2024