A046332 Palindromes with exactly 6 prime factors (counted with multiplicity).

2772, 2992, 6776, 8008, 21112, 21712, 21912, 23632, 23832, 25452, 25752, 25952, 27472, 28782, 29392, 40104, 40304, 40404, 42024, 42924, 44044, 44144, 44744, 44944, 45954, 46764, 46864, 48984, 53235, 54945, 55755, 59895, 60606, 61216

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A002113 (palindromes), A046306 (bigomega = 6), A046319.

Cf. A046396 (similar but terms must be squarefree), A373466 (similar, but only distinct prime divisors are counted).

Programs

Maple

N:= 6: # to get all terms of up to N digits
digrev:= proc(n) local L,Ln; L:= convert(n,base,10);Ln:= nops(L);
add(L[i]*10^(Ln-i),i=1..Ln);
end proc:
Res:= NULL:
for d from 2 to N do
  if d::even then
    m:= d/2;
    Res:= Res, select(numtheory:-bigomega=6,
           [seq](n*10^m + digrev(n), n=10^(m-1)..10^m-1));
  else
    m:= (d-1)/2;
    Res:= Res, select(numtheory:-bigomega=6,
           [seq](seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1));
  fi
od:
map(op,[Res]); # Robert Israel, Dec 23 2014

PARI

A046332_upto(N, start=1, num_fact=6)={ my(L=List()); while(N >= start = nxt_A002113(start), bigomega(start)==num_fact && listput(L, start)); L} \\ M. F. Hasler, Jun 06 2024

Python

from sympy import factorint
def palQgen10(l): # generator of palindromes in base 10 of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1,l+1):
            for y in range(10**(x-1),10**x):
                s = str(y)
                yield int(s+s[-2::-1])
            for y in range(10**(x-1),10**x):
                s = str(y)
                yield int(s+s[::-1])
A046332_list = [x for x in palQgen10(4) if sum(list(factorint(x).values())) == 6]
# Chai Wah Wu, Dec 21 2014

Formula

Intersection of A002113 and A046306. - M. F. Hasler, Jun 06 2024