A355305 Carmichael numbers ending in 5.

1105, 2465, 10585, 62745, 278545, 449065, 825265, 1050985, 2531845, 3224065, 3664585, 5632705, 6054985, 9582145, 11119105, 12945745, 13187665, 13992265, 15403285, 21584305, 22665505, 28787185, 31692805, 36121345, 37354465, 39353665, 40280065, 41298985, 47006785, 60112885, 67371265, 74165065, 84417985

Offset: 1

Author

Omar E. Pol, Jul 03 2022

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to Carmichael numbers

Crossrefs

Intersection of A002997 and A017329.

Cf. A352970, A354609, A355307, A355309.

Programs

Mathematica

Select[10*Range[0, 10^7] + 5, CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] &] (* Amiram Eldar, Jul 07 2022 *)

PARI

Korselt(n) = my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1;
isok(n) = ((n%10)==5) && !isprime(n) && Korselt(n) && n>1; \\ Michel Marcus, Jul 07 2022; after A002997

Python

from itertools import islice
from sympy import factorint, nextprime
def A355305_gen(): # generator of terms
    p, q = 3, 5
    while True:
        for n in range(p+2+(-p+3)%10, q, 10):
            f = factorint(n)
            if max(f.values()) == 1 and not any((n-1) % (p-1) for p in f):
                yield n
        p, q = q, nextprime(q)
A355305_list = list(islice(A355305_gen(),10)) # Chai Wah Wu, Jul 24 2022