login
A387460
Composite cyclic numbers (subset of A050384) that are of the form 4n+1.
3
33, 65, 69, 77, 85, 133, 141, 145, 161, 177, 185, 209, 213, 217, 221, 249, 265, 321, 329, 341, 345, 365, 377, 393, 413, 437, 445, 469, 473, 481, 485, 493, 501, 517, 533, 537, 545, 553, 561, 565, 573, 581, 589, 629, 649, 665, 681, 685, 697, 705, 713, 717, 721, 745, 749, 753
OFFSET
1,1
EXAMPLE
The first term, 33, is cyclic because phi(33)=20 (the number of positive integers less than or equal to 33 that are relatively prime to 33) and gcd(33, phi(33)) = 1. Also 33 is composite because 33 = 3 * 11. Also 33 is congruent to 1 mod 4 because 33 = 4*8+1.
MAPLE
q:= n-> not isprime(n) and igcd(n, numtheory[phi](n))=1:
select(q, [4*i+1$i=1..190])[]; # Alois P. Heinz, Sep 04 2025
# Alternative:
isA387460 := proc(n)
not isprime(n) and isA003277(n) and modp(n, 4) =1 ;
end proc:
A387460 := proc(n)
option remember ;
if n =1 then
33 ;
else
for a from procname(n-1)+4 do
if isA387460(a) then
return a;
end if;
end do:
end if;
end proc:
seq(A387460(n), n=1..100) ; # R. J. Mathar, Mar 18 2026
MATHEMATICA
Select[Range[1, 1000, 4], CompositeQ[#] && CoprimeQ[#, EulerPhi[#]] &] (* Amiram Eldar, Aug 29 2025 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joel E. Cohen, Aug 29 2025
STATUS
approved