A105648
Smallest member of a set of Smith triples.
Original entry on oeis.org
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
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.
-
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 *)
A105649
Smallest member of set of 4 consecutive numbers which are Smith numbers.
Original entry on oeis.org
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
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.
-
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 *)
a(7) inserted and more terms added by
Amiram Eldar, Aug 18 2020
A235812
a(n) is the start of the earliest run of n numbers such that the sum of their digits is equal to the sum of the digits of their prime factors.
Original entry on oeis.org
2, 2, 2, 2, 1458855, 1790478, 429990136, 4475873320, 1979414080360
Offset: 1
The four numbers 2, 3, 4, 5 are either prime (2, 3, 5) or Smith (4) numbers. In any case, the sum of their digits is equal to the sum of their prime factors (counted with multiplicity), hence a(1) = a(2) = a(3) = a(4) = 2.
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