A105648 Smallest member of a set of Smith triples.

73615, 209065, 225951, 283745, 305455, 342879, 656743, 683670, 729066, 747948, 774858, 879221, 954590, 1185547, 1262722, 1353955, 1369374, 1495718, 1622495, 1666434, 1790480, 2197579, 2299772, 2428854, 2561678, 2576441, 2580367, 2636516, 2665480, 2707580, 2741816

Offset: 1

Author

Shyam Sunder Gupta, May 03 2005

Keywords

• nonn
• base

Comments

If there are 3 consecutive numbers which are Smith numbers, these can be called a Smith triple.

Examples

			a(1) = 73615 because 73615 is the smallest of 3 consecutive integers which are Smith numbers, i.e., the three consecutive numbers 73615, 73616, 73617 are all Smith numbers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• S. S. Gupta, Smith Numbers.

Crossrefs

Cf. A006753, A050219, A059754, A105649, A105650.

Programs

Mathematica

digSum[n_] := Plus @@ IntegerDigits[n]; smithQ[n_] := CompositeQ[n] && Plus @@ (Last@#*digSum[First@#] & /@ FactorInteger[n]) == digSum[n]; sm = smithQ /@ Range[3]; seq = {}; Do[sm = Join[Rest[sm], {smithQ[k]}]; If[And @@ sm, AppendTo[seq, k - 2]], {k, 4, 10^6}]; seq (* Amiram Eldar, Aug 18 2020 *)

Extensions

More terms from Amiram Eldar, Aug 18 2020