login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A306452 Pseudoprimes to base 3 that are not squarefree, including the non-coprime pseudoprimes. 2
121, 726, 3751, 4961, 7381, 11011, 29161, 32791, 142901, 228811, 239701, 341341, 551881, 566401, 595441, 671671, 784201, 856801, 1016521, 1053426, 1237951, 1335961, 1433971, 1804231, 1916761, 2000251, 2254351, 2446741, 2817001, 2983981, 3078361, 3307051, 3562361 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers k such that 3^k == 3 (mod k) and k is divisible by the square of a Mirimanoff prime (or base-3 Wieferich prime), A014127.
A non-coprime pseudoprime in base b is a number k such that b^k == b (mod k) and that gcd(b, k) > 1, and the non-coprime pseudoprime in base 3 (726, 1053426, 6498426, ...) that are not squarefree are listed in A306450 while the others terms in this sequence (121, 3751, 4961, ...) are listed in A244065. So this sequence is the union of A244065 and A306450.
Intersection of A122780 and A013929.
LINKS
EXAMPLE
121 is a term because 3^120 == (3^5)^24 == 1 (mod 121) and 121 = 11^2.
Although 3^725 = 243 rather than 1 mod 726, we see that nevertheless 3^726 = 3 mod 726, and since 726 = 2 * 3 * 11^2, 726 is in the sequence. - Alonso del Arte, Mar 16 2019
MATHEMATICA
Select[Range[5000], PowerMod[3, #, #] == 3 && MoebiusMu[#] == 0 &] (* Alonso del Arte, Mar 16 2019 *)
PROG
(PARI) forcomposite(n=1, 10^7, if(Mod(3, n)^n==3 && !issquarefree(n), print1(n, ", ")))
CROSSREFS
Sequence in context: A293566 A293507 A356630 * A238250 A361658 A293588
KEYWORD
nonn
AUTHOR
Jianing Song, Feb 17 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 22:15 EDT 2024. Contains 371282 sequences. (Running on oeis4.)