A371696 Composite numbers that divide the reverse of the concatenation of their ascending order prime factors, with repetition.

26, 38, 46, 378, 26579, 84941, 178838, 30791466, 39373022, 56405502, 227501395, 904085931, 1657827142

Offset

1,1

Comments

a(14) > 10^10, if it exists. - Daniel Suteu, Apr 28 2024

Links

Table of n, a(n) for n=1..13.

Example

26 is a term as 26 = 2 * 13 = "213" which is reverse is "312", and 312 is divisible by 26.
227501395 is a term as 227501395 = 5 * 11 * 17 * 23 * 71 * 149 = "511172371149" which in reverse is "941173271115", and 941173271115 is divisible by 227501395.

Prog

(Python)
from itertools import count, islice
from sympy import isprime, factorint
def ok(k): return not isprime(k) and int("".join(str(p)[::-1]*e for p, e in list(factorint(k).items())[::-1]))%k == 0
def agen(): yield from filter(ok, count(4))
print(list(islice(agen(), 7))) # Michael S. Branicky, Apr 13 2024
(Python)
from itertools import count, islice
from sympy import factorint
def A371696_gen(startvalue=4): # generator of terms >= startvalue
    for n in count(max(startvalue, 4)):
        f = factorint(n)
        if sum(f.values()) > 1:
            c = 0
            for p in sorted(f, reverse=True):
                a = pow(10, len(s:=str(p)), n)
                q = int(s[::-1])
                for _ in range(f[p]):
                    c = (c*a+q)%n
            if not c:
                yield n
A371696_list = list(islice(A371696_gen(), 6)) # Chai Wah Wu, Apr 13 2024

Crossrefs

Cf. A027746, A037276, A259047, A371641, A371666.

Sequence in context: A045092 A106551 A106553 * A178662 A039324 A043147

Adjacent sequences: A371693 A371694 A371695 * A371697 A371698 A371699

Keyword

nonn,base,more

Author

Scott R. Shannon, Apr 03 2024

Extensions

a(13) from Daniel Suteu, Apr 28 2024

Status

approved