A356750 Palindromic odd numbers with an odd number of distinct prime factors.

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

Michael S. Branicky, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A356747 A356748 A356749 * A356751 A356752 A356753

Keyword

nonn,base

Author

Tanya Khovanova, Aug 25 2022

Status

approved