A182089 Numbers of the form (330*k+7)*(660*k+13)*(990*k+19)*(1980*k+37).

63973, 461574735553, 7103999557333, 35498632881313, 111463190499493, 271061745643873, 560604728986453, 1036648928639233, 1765997490154213, 2825699916523393, 4303052068178773, 6295596162992353, 8911120776276133, 12267660840782113, 16493497646702293

Offset

1,1

Comments

Conjecture: C = (330k+7)*(660k+13)*(990k+19)*(1980k+37) is a Carmichael number if 330k+7, 660k+13, 990k+19 and 1980k+37 are all four prime numbers. [The conjecture is true, and can be proved using Korselt's criterion. - Amiram Eldar, Apr 24 2024]

For 0<k<50 the condition is satisfied just for k = 0 and k = 1.

The next term is > 10^19.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Index entries for sequences related to Carmichael numbers.

Mathematica

Table[(330 n + 7)*(660 n + 13)*(990 n + 19)*(1980 n + 37), {n, 0, 50}] (* G. C. Greubel, Aug 20 2017 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {63973, 461574735553, 7103999557333, 35498632881313, 111463190499493}, 20] (* Vincenzo Librandi, Aug 21 2017 *)

Prog

(PARI) a(k)=(330*k+7)*(660*k+13)*(990*k+19)*(1980*k+37) \\ Charles R Greathouse IV, Jun 30 2017
(Magma) [(330*n+7)*(660*n+13)*(990*n+19)*(1980*n+37): n in [0..15]]; // Vincenzo Librandi, Aug 21 2017

Crossrefs

Cf. A002997 (Carmichael numbers).

Sequence in context: A290793 A182518 A317136 * A217126 A250823 A054738

Adjacent sequences: A182086 A182087 A182088 * A182090 A182091 A182092

Keyword

nonn,easy

Author

Marius Coman, Apr 11 2012

Status

approved