A105649 Smallest member of set of 4 consecutive numbers which are Smith numbers.

4463535, 6356910, 8188933, 9425550, 11148564, 15966114, 15966115, 18542654, 21673542, 22821992, 23767287, 28605144, 36615667, 39227466, 47096634, 47395362, 48072396, 54054264, 55464835, 57484614, 57756450, 57761165, 58418508, 61843387, 62577157, 64572186, 65484066

Offset: 1

Author

Shyam Sunder Gupta, May 03 2005

Keywords

• nonn
• base

Examples

			a(1) = 4463535 because 4463535 is the smallest member of a set of 4 consecutive numbers which are Smith numbers i.e. four consecutive numbers 4463535, 4463536, 4463537, 4463538 are all Smith numbers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• S. S. Gupta, Smith Numbers.

Crossrefs

Cf. A006753, A050219, A059754, A105648, A105650.

Programs

Mathematica

digSum[n_] := Plus @@ IntegerDigits[n]; smithQ[n_] := CompositeQ[n] && Plus @@ (Last @#* digSum[First@#] & /@ FactorInteger[n]) == digSum[n]; sm = smithQ /@ Range[4]; seq = {}; Do[sm = Join[Rest[sm], {smithQ[k]}]; If[And @@ sm, AppendTo[seq, k - 3]], {k, 5, 10^7}]; seq (* Amiram Eldar, Aug 18 2020 *)

Extensions

a(7) inserted and more terms added by Amiram Eldar, Aug 18 2020