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Numbers k such that no Paley-type Hadamard matrix of order k exists.
1

%I #21 Mar 05 2023 11:01:37

%S 92,116,156,172,184,188,232,236,260,268,292,324,356,372,376,404,412,

%T 428,436,452,472,476,508,520,532,536,584,596,604,612,652,668,712,716,

%U 732,756,764,772,808,836,852,856,872,876,892,904,932,940,944,952,956

%N Numbers k such that no Paley-type Hadamard matrix of order k exists.

%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HadamardMatrix.html">Hadamard Matrix</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PaleyClass.html">Paley Class</a>.

%F Divisible by 4 but not of form 2^a*(q+1), q = odd prime power.

%o (PARI) isp(k) = for (i=0, valuation(k, 2), if (isprimepower(k/2^i-1, &p) && (p%2), return(1));); return(0);

%o isok(k) = !(k%4) && !isp(k); \\ _Michel Marcus_, Mar 05 2023

%Y Subsequence of A008586.

%K nonn

%O 1,1

%A _Eric W. Weisstein_