OFFSET
1,1
COMMENTS
Is it true that no terms end with 1? A separate search on those shows none with < 70 digits. Michael S. Branicky, Apr 23 2024
Testing all products of repunit primes (A004022, A004023), there are no terms ending in 1 less than 10^3000. - Michael S. Branicky, Apr 24 2024
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..197 (all terms with <= 21 digits)
EXAMPLE
The initial terms and their factorizations are:
4 = [2, 2]
8 = [2, 2, 2]
9 = [3, 3]
22 = [2, 11]
32 = [2, 2, 2, 2, 2]
33 = [3, 11]
44 = [2, 2, 11]
55 = [5, 11]
64 = [2, 2, 2, 2, 2, 2]
77 = [7, 11]
88 = [2, 2, 2, 11]
93 = [3, 31]
99 = [3, 3, 11]
422 = [2, 211]
633 = [3, 211]
775 = [5, 5, 31]
844 = [2, 2, 211]
933 = [3, 311]
993 = [3, 331]
4222 = [2, 2111]
4442 = [2, 2221]
6333 = [3, 2111]
6655 = [5, 11, 11, 11]
6663 = [3, 2221]
7533 = [3, 3, 3, 3, 3, 31]
7744 = [2, 2, 2, 2, 2, 2, 11, 11]
...
PROG
(Python)
from sympy import factorint
def ni(s): return sorted(s, reverse=True) == list(s)
def ok(n):
if n < 4 or is_prime(n): return False
s, f = str(n), "".join(str(p)*e for p, e in factorint(n).items())
return ni(s+f)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Apr 23 2024
(Python) # faster for initial segment of sequence
from sympy import isprime
from itertools import count, islice, combinations_with_replacement as mc
def ni(s): return s == "".join(sorted(s, reverse=True))
def bgen(d):
yield from ("".join(m) for m in mc("987654321", d))
def agen(): # generator of terms
for d in range(1, 70):
out = set()
for s in bgen(d):
t = int(s)
if t < 4 or is_prime(t): continue
if ni(s+"".join(str(p)*e for p, e in factorint(t).items())):
out.add(t)
yield from sorted(out)
print(list(islice(agen(), 50))) # Michael S. Branicky, Apr 23 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon, Apr 16 2024.
STATUS
approved