A104171 Reversible Smith numbers, i.e., Smith numbers whose reversal is also a Smith number.

4, 22, 58, 85, 121, 202, 265, 319, 454, 535, 562, 636, 666, 913, 1111, 1507, 1642, 1881, 1894, 1903, 2461, 2583, 2605, 2614, 2839, 3091, 3663, 3852, 4162, 4198, 4369, 4594, 4765, 4788, 4794, 4954, 4974, 4981, 5062, 5386, 5458, 5539, 5674, 5818, 5926, 6295

Offset: 1

Author

Shyam Sunder Gupta, Mar 10 2005

Keywords

• nonn
• base

Comments

The palindromic Smith numbers (A098834) are a subset of the reversible Smith numbers.

Examples

			a(3) = 58 because 58 and its reverse 85 are Smith numbers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Shyam Sunder Gupta, Smith Numbers.
• Shyam Sunder Gupta, Smith Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 4, 127-157.

Crossrefs

Cf. A006753, A098834.

Programs

Mathematica

rev[n_] := FromDigits @ Reverse @ IntegerDigits[n]; digSum[n_] := Plus @@ IntegerDigits[n]; smithQ[n_] := CompositeQ[n] && Plus @@ (Last@#*digSum[First@#] & /@ FactorInteger[n]) == digSum[n]; Select[Range[6000], smithQ[#] && smithQ @ rev[#] &] (* Amiram Eldar, Aug 24 2020 *)

Python

from sympy import factorint
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 ok(n): return smith(n) and smith(int(str(n)[::-1]))
print(list(filter(ok, range(6296)))) # Michael S. Branicky, Apr 22 2021