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A356750
Palindromic odd numbers with an odd number of distinct prime factors.
2
3, 5, 7, 9, 11, 101, 121, 131, 151, 181, 191, 313, 343, 353, 373, 383, 525, 555, 585, 595, 727, 757, 777, 787, 797, 919, 929, 969, 1001, 1221, 1331, 1551, 1771, 1881, 3333, 3553, 3663, 5225, 5335, 5445, 5555, 5665, 5885, 5995, 7007, 7227, 7337, 7557, 7667, 7777, 7887, 9339, 9669, 9779, 9889, 9999, 10201, 10301
OFFSET
1,1
COMMENTS
Numbers in this sequence can be divided by nontrivial prime powers.
This sequence contains palindromic primes: A002385.
This sequence contains palindromic odd composite numbers that are products of an odd number of distinct primes: A075808.
LINKS
EXAMPLE
Number 525 = 3*5^2*7 has 3 prime factors 3, 5, and 7. Thus, it is in the sequence.
MATHEMATICA
Select[Range[2, 12000], OddQ[#] && PalindromeQ[#] && OddQ[Length[Transpose[FactorInteger[#]][[2]]]] &]
PROG
(Python)
from sympy import isprime, factorint
from itertools import count, islice, product
def cond(n): return n&1 and (isprime(n) or len(factorint(n))&1)
def oddpals(): # generator of odd palindromes
yield from [1, 3, 5, 7, 9]
for d in count(2):
for first in "13579":
for p in product("0123456789", repeat=(d-2)//2):
left = "".join(p); right = left[::-1]
for mid in [[""], "0123456789"][d%2]:
yield int(first + left + mid + right + first)
def agen(): yield from filter(cond, oddpals())
print(list(islice(agen(), 58))) # Michael S. Branicky, Aug 25 2022
(PARI) ispal(n) = my(d1=digits(n)); d1 == Vecrev(d1)
forstep(k=3, 10^6, 2, if(ispal(k)&&omega(k)%2==1, print1(k, ", "))) \\ Alexandru Petrescu, Sep 10 2022
CROSSREFS
Sequence in context: A061507 A046497 A061512 * A083964 A340439 A131628
KEYWORD
nonn,base
AUTHOR
Tanya Khovanova, Aug 25 2022
STATUS
approved