A261534 Nonprime palindromes n with only the digits 0, 1, 2 such that the product of divisors of n is also a palindrome.
1, 22, 111, 121, 202, 1001, 1111, 10001, 10201, 11111, 100001, 1000001, 1001001, 1012101, 1100011, 1101011, 1111111, 10000001, 100000001, 101000101, 110000011, 200010002, 10000000001, 10011111001, 11000100011, 11001010011, 11100100111, 11101010111, 20000100002
Offset: 1
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..203
Programs
-
Mathematica
lim = 1000000; palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; c = Complement[Range@ lim, Prime@ Range@ PrimePi@ lim]; t = Select[c, Total@ Take[RotateRight@ DigitCount@ #, -7] == 0 &]; Select[t, palQ[Times @@ Divisors@ #] &] (* Michael De Vlieger, Sep 02 2015 *) Rest[Select[FromDigits/@Tuples[{0,1,2},11],!PrimeQ[#]&&AllTrue[{#,Times@@ Divisors[ #]},PalindromeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 02 2020 *) -
Python
from _future_ import division from sympy import divisor_count from gmpy2 import isqrt, t_divmod, digits def palgen(l,b=10): # generator of palindromes in base b of length <= 2*l if l > 0: yield 0 for x in range(1,l+1): n = b**(x-1) n2 = n*b for y in range(n,n2): k, m = y//b, 0 while k >= b: k, r = t_divmod(k,b) m = b*m + r yield y*n + b*m + k for y in range(n,n2): k, m = y, 0 while k >= b: k, r = t_divmod(k,b) m = b*m + r yield y*n2 + b*m + k A261534_list = [1] for m in palgen(17,3): n = int(digits(m,3)) d = int(divisor_count(n)) if d > 2: q, r = t_divmod(d,2) s = digits(n**q*(isqrt(n) if r else 1)) if s == s[::-1]: A261534_list.append(n)
Comments