A383487 Prime powers p^r such that p == 3 (mod 4) and r is even.

9, 49, 81, 121, 361, 529, 729, 961, 1849, 2209, 2401, 3481, 4489, 5041, 6241, 6561, 6889, 10609, 11449, 14641, 16129, 17161, 19321, 22801, 26569, 27889, 32041, 36481, 39601, 44521, 49729, 51529, 57121, 59049, 63001, 69169, 73441, 80089, 94249, 96721, 109561, 117649

Offset

1,1

Comments

Allowed orders (vertex counts) of Peisert graphs.

Links

Bruce Nye, Table of n, a(n) for n = 1..5000

Wojciech Peisert, All Self-Complementary Symmetric Graphs, J. Algebra, 240 (2001), 209-229.

Eric Weisstein's World of Mathematics, Peisert Graph.

Maple

N:= 10^6: # for terms <= N
P:= select(isprime, [seq(i, i=3..floor(sqrt(N)), 4)]);
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

Mathematica

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

Prog

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

Crossrefs

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

Subsequence of A056798.

Sequence in context: A137175 A167744 A028375 * A032598 A352141 A110873

Adjacent sequences: A383484 A383485 A383486 * A383488 A383489 A383490

Keyword

nonn

Author

Eric W. Weisstein, Apr 30 2025

Extensions

More terms from Bruce Nye, May 17 2026

Status

approved