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

1,1

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

S. S. Gupta, Smith Numbers.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A006753, A098834.

Sequence in context: A076525 A089761 A098837 * A036924 A130015 A189953

Adjacent sequences: A104168 A104169 A104170 * A104172 A104173 A104174

Keyword

nonn,base

Author

Shyam Sunder Gupta, Mar 10 2005

Status

approved