A255514 - OEIS

%I #27 Apr 24 2024 02:44:08

%S 46657,25505418241,42780070657,73543985857,116355401857,262757672641,

%T 347138711137,524866954177,687990546721,4170876528961,5535042490657,

%U 9461608786657,10620849817441,13685652197857,23802444500257,27407538845857,31566404586817,39638503707841

%N Carmichael numbers of the form (24*k+13)*(72*k+37)*(192*k+97), where 24*k+13, 72*k+37 and 192*k+97 are all primes.

%H Amiram Eldar, <a href="/A255514/b255514.txt">Table of n, a(n) for n = 1..10000</a>

%H Umberto Cerruti, <a href="/A255514/a255514.pdf">Pseudoprimi di Fermat e numeri di Carmichael</a> (in Italian), p. 12.

%H <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.

%t f[k_] := {24*k + 13, 72*k + 37, 192*k + 97}; Times @@ f[#]& /@ Select[Range[0, 500], And @@ PrimeQ[f[#]] &] (* _Amiram Eldar_, Apr 24 2024 *)

%o (Magma) [(24*n+13)*(72*n+37)*(192*n+97): n in [0..500] | IsPrime(24*n+13) and IsPrime(72*n+37) and IsPrime(192*n+97)];

%o (PARI) lista(kmax) = for(k = 0, kmax, if(isprime(24*k + 13) && isprime(72*k + 37) && isprime(192*k + 97), print1((24*k+13)*(72*k+37)*(192*k+97), ", "))); \\ _Amiram Eldar_, Apr 24 2024

%Y Cf. A002997, A255513 (associated k).

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Feb 25 2015

%E Corrected and extended by _Bruno Berselli_, Feb 25 2015