A383487 - OEIS

%I #45 May 20 2026 23:43:36

%S 9,49,81,121,361,529,729,961,1849,2209,2401,3481,4489,5041,6241,6561,

%T 6889,10609,11449,14641,16129,17161,19321,22801,26569,27889,32041,

%U 36481,39601,44521,49729,51529,57121,59049,63001,69169,73441,80089,94249,96721,109561,117649

%N Prime powers p^r such that p == 3 (mod 4) and r is even.

%C Allowed orders (vertex counts) of Peisert graphs.

%H Bruce Nye, <a href="/A383487/b383487.txt">Table of n, a(n) for n = 1..5000</a>

%H Wojciech Peisert, <a href="https://doi.org/10.1006/jabr.2000.8714">All Self-Complementary Symmetric Graphs</a>, J. Algebra, 240 (2001), 209-229.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PeisertGraph.html">Peisert Graph</a>.

%p N:= 10^6: # for terms <= N

%p P:= select(isprime,[seq(i,i=3..floor(sqrt(N)),4)]);

%p sort(map(proc(p) local i;  seq(p^(2*i), i=1..floor(log[p^2](N))) end proc, P)); # _Robert Israel_, Apr 30 2025

%t Select[Range[10^5], MatchQ[FactorInteger[#], {{p_ /; Mod[p, 4] == 3, _?EvenQ}}] &]

%o (PARI) apply(sqr, select(x->(eulerphi(2*x)/2)%2==1, [3..345])) \\ _Bruce Nye_, May 13 2026

%Y Cf. A197504 (square root), A002145 (4*k+3 primes).

%Y Subsequence of A056798.

%K nonn

%O 1,1

%A _Eric W. Weisstein_, Apr 30 2025

%E More terms from _Bruce Nye_, May 17 2026