cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

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Author

Shyam Sunder Gupta, May 03 2005

Keywords

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.
		

Crossrefs

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

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

Views

Author

Shyam Sunder Gupta, May 03 2005

Keywords

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.
		

Crossrefs

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

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

Views

Author

Giovanni Resta, Jan 16 2014

Keywords

Comments

This sequence takes into account both primes and Smith numbers (A006753).
a(10) > 5*10^12.

Examples

			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.
		

Crossrefs

Showing 1-3 of 3 results.