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A256074
Squares representable as k*m + k + m, where k >= m > 1 are squares.
1
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
1,1
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
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10657 (terms <= 10^16)
EXAMPLE
a(1) = 49 = 4*9 + 4 + 9.
a(2) = 169 = 9*16 + 9 + 16.
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Mar 14 2015
EXTENSIONS
More terms from David A. Corneth, Oct 19 2024
STATUS
approved