A098834 Palindromic Smith numbers.

4, 22, 121, 202, 454, 535, 636, 666, 1111, 1881, 3663, 7227, 7447, 9229, 10201, 17271, 22522, 24142, 28182, 33633, 38283, 45054, 45454, 46664, 47074, 50305, 51115, 51315, 54645, 55055, 55955, 72627, 81418, 82628, 83038, 83938, 90409, 95359, 96169, 164461

Offset

1,1

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Example

a(3) = 121 because 121 is a Smith number as well as a palindromic number.

Mathematica

d[n_] := IntegerDigits[n]; tr[n_] := Transpose[FactorInteger[n]]; Select[Range[2, 1.7*10^5], !PrimeQ[#] && Reverse[x=d[#]] == x && Total[x] == Total[d@tr[#][[1]]*tr[#][[2]], 2]&] (* Jayanta Basu, Jun 04 2013 *)

Prog

(Python)
from sympy import factorint
from itertools import product
def sd(n): return sum(map(int, str(n)))
def smith(n):
  f = factorint(n)
  return sum(f[p] for p in f) > 1 and sd(n) == sum(sd(p)*f[p] for p in f)
def palsto(limit):
  yield from range(min(limit, 9)+1)
  midrange = [[""], [str(i) for i in range(10)]]
  for digs in range(2, 10**len(str(limit))):
    for p in product("0123456789", repeat=digs//2):
      left = "".join(p)
      if left[0] == '0': continue
      for middle in midrange[digs%2]:
        out = int(left + middle + left[::-1])
        if out > limit: return
        yield out
print(list(filter(smith, palsto(164461)))) # Michael S. Branicky, Apr 22 2021

Crossrefs

Cf. A006753.

Subsequence of A104171. Supersequence of A104166.

Sequence in context: A244900 A261193 A025569 * A065983 A236576 A185858

Adjacent sequences: A098831 A098832 A098833 * A098835 A098836 A098837

Keyword

base,nonn

Author

Shyam Sunder Gupta, Oct 10 2004

Status

approved