A206347 Numbers n such that 10*n+1, 20*n+1, and 30*n+1 are all primes.

21, 27, 33, 60, 117, 153, 222, 228, 306, 426, 480, 495, 558, 585, 615, 636, 669, 684, 762, 768, 819, 852, 894, 909, 1083, 1125, 1131, 1224, 1239, 1341, 1455, 1512, 1539, 1776, 1812, 1845, 2301, 2484, 2517, 2541, 2604, 2706, 2769, 3093, 3177

Offset: 1

Author

José María Grau Ribas, Feb 06 2012

Keywords

• nonn

Comments

(10*n+1)*(20*n+1)*(30*n+1) is a Carmichael number for all n in this sequence. Why is (6m+1)*(12m+1)*(18m +1) used to generate Carmichael numbers and never the formula (10m+1)*(20m+1)*(30m+1)?

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002997, A046025.

Programs

Mathematica

Select[Range[20000], PrimeQ[10 #+1] && PrimeQ[20 #+1] && PrimeQ[30 #+1]&]
Select[Range[3500],AllTrue[1+{1,2,3}10#,PrimeQ]&]  (* Harvey P. Dale, May 18 2025 *)