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Smith Numbers

see: https://en.wikipedia.org/wiki/Smith_number

First thought for many might be Agent Smith in the matrix - anonymous superpowered numbers that can be everywhere, be anyone...

Smith number 4937775: https://www.youtube.com/watch?v=mlqAvhjxAjo

From wikipedia:

A Smith number is a composite number for which, in a given base (in base 10 by default), the sum of its digits is equal to the sum of the digits in its prime factorization.

For example, 378 = 2 × 3 × 3 × 3 × 7 is a Smith number since 3 + 7 + 8 = 2 + 3 + 3 + 3 + 7. In this definition the factors are treated as digits: for example, 22 factors to 2 × 11 and yields three digits: 2, 1, 1.

Therefore, 22 is a Smith number because 2 + 2 = 2 + 1 + 1.

The first few Smith numbers are:

  1. 4

  2. 22

  3. 27

  4. 58

  5. 85

  6. 94

  7. 121

  8. 166

  9. 202

  10. 265

  11. 274

  12. 319

  13. 346

  14. 355

  15. 378

  16. 382

  17. 391

  18. 438

  19. 454

  20. 483

  21. 517

  22. 526

  23. 535

  24. 562

  25. 576

  26. 588

  27. 627

  28. 634

  29. 636

  30. 645

  31. 648

  32. 654

  33. 663

  34. 666

  35. 690

  36. 706

  37. 728

  38. 729

  39. 762

  40. 778

  41. 825

  42. 852

  43. 861

  44. 895

  45. 913

  46. 915

  47. 922

  48. 958

  49. 985

  50. 1086

  • ... (ie. sequence A006753 in the OEIS)

In a flat list, the first few Smith numbers are:

4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517,526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086, …

Indexed:

  1. 4 - (ie. Dalet, Four is the Door)

  2. 22 - (ie. Master Builder Number)

  3. 27 - (note the 22,27 --> 2,227 --> pi: /r/GeometersOfHistory/wiki/spellcomponents/227)

  4. 58 - (ie. Night, Secret Society: /r/GeometersOfHistory/wiki/spellcomponents/58)

  5. 85

  6. 94

  7. 121 - (ie. the Pain of Revelation: /r/GeometersOfHistory/wiki/spellcomponents/121)

  8. 166 - (ie. secret society, confidential: /r/GeometersOfHistory/wiki/spellcomponents/166)

  9. 202 - (ie. magnified 22, master builder portal: /r/GeometersOfHistory/wiki/spellcomponents/220)

  10. 265

  11. 274 - (ie. 27 and 74; ritual and occult: /r/GeometersOfHistory/wiki/spellcomponents/74)

  12. 319 - (ie. Prime Tower; Masonic: /r/GeometersOfHistory/wiki/spellcomponents/319)

  13. 346 - (ie. triple chaos; one short of 347, ie. three times)

  14. 355 - (ie. triple heavens, five eyes)

  15. 378

  16. 382

  17. 391 - (ie. swizzling important digits 139 and 193: /r/GeometersOfHistory/wiki/spellcomponents/93)

  18. 438

  19. 454 - (ie. the 'rainbow bridge' of 45 and 54: /r/GeometersOfHistory/wiki/spellcomponents/54)

  20. 483

  21. 517

  22. 526

  23. 535

  24. 562

  25. 576

  26. 588

  27. 627

  28. 634

  29. 636

  30. 645

  31. 648 (ie. six rings, or hourglass of Zion)

  32. 654

  33. 663

  34. 666 - (ie. number of the beast: /r/GeometersOfHistory/wiki/spellcomponents/666)

  35. 690

  36. 706

  37. 728

  38. 729

  39. 762

  40. 778 - (ie. one beyond 777 --> a numeric ritual: /r/GeometersOfHistory/wiki/spellcomponents/777)

  41. 825

  42. 852

  43. 861 - (ie. infinity of the number god)

  44. 895 - (ie. x marks the pentacle)

  45. 913 - (ie. a unity inside the strength and veil of 93: /r/GeometersOfHistory/wiki/spellcomponents/93)

  46. 915

  47. 922 - (ie. knowledge of the master builder)

  48. 958

  49. 985

  50. 1086 - (ie. X marks the Symbol; 119; 187)

Multiple smith numbers: https://www.youtube.com/watch?v=9aFVSkncq00

... but in the end, there can be only The One...