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%I #18 Oct 19 2024 22:03:38
%S 49,169,324,441,961,1849,2209,3249,5329,8281,12321,15129,17424,17689,
%T 24649,33489,44521,58081,58564,64009,65025,74529,94249,103684,117649,
%U 145161,177241,191844,214369,237169,257049,305809,361201,423801,480249,494209,573049,660969,700569
%N Squares representable as k*m + k + m, where k >= m > 1 are squares.
%C A subsequence of A254671.
%C 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.
%C 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
%H David A. Corneth, <a href="/A256074/b256074.txt">Table of n, a(n) for n = 1..10657</a> (terms <= 10^16)
%e a(1) = 49 = 4*9 + 4 + 9.
%e a(2) = 169 = 9*16 + 9 + 16.
%o (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
%Y Cf. A000290, A058031, A066938, A254671.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, Mar 14 2015
%E More terms from _David A. Corneth_, Oct 19 2024