A243582 - OEIS

%I #13 Dec 18 2023 09:50:12

%S 7,15,23,31,47,55,103

%N Integers of the form 8k+7 (A004771) that cannot be written as sum of four distinct squares.

%H J. O. Sizemore, <a href="http://www.math.wisc.edu/~josizemore/Notes16%284-square%29.pdf">Lagrange's Four Square Theorem</a>

%H R. C. Vaughan, <a href="https://personal.science.psu.edu/rcv4/Foursq.pdf">Lagrange's four-square theorem</a>

%H Eric Weisstein's World of Math, <a href="http://mathworld.wolfram.com/LagrangesFour-SquareTheorem.html">Lagrange's Four-Square Theorem</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem">Lagrange's four-square theorem</a>

%e a(6) = 55 since 55 == 7 (mod 8) and all its representations as a sum of squares have duplicates, namely, 55=1^2+1^2+2^2+7^2, 55=1^2+2^2+5^2+5^2, 55=1^2+3^2+3^2+6^2.

%Y Cf. A001948, A004771, A008586, A016813, A016825, A004767, A243577, A243578, A243579, A243580, A243581.

%K nonn,fini,full

%O 1,1

%A _Walter Kehowski_, Jun 08 2014