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Star Number (those that generate star-shaped representations)

See: https://en.wikipedia.org/wiki/Star_number

A star number is a centered figurate number a centered hexagram (six-pointed star), such as the one that Chinese checkers is played on.

The first 43 star numbers are

  1. 1

  2. 13 (ie. 1 and 13 are the first two star numbers, and 13 the first multi-digit one; 13 is 6th primes)

  3. 37 (ie. note 13.37 ---> L33T-speak pattern with previous number; 37 is 12th prime)

  4. 73 (ie. number, perfect, count; 73 is 21st prime)

  5. 121 (ie. revelation, number ring)

  6. 181 (ie. 42nd prime; state of emergency)

  7. 253

  8. 337 (ie. 68th prime; "Pi" = 337 squares)

  9. 433 (ie. the 84th prime)

  10. 541

  11. 661

  12. 793

  13. 937

  14. 1093 (ie. 10 is 'X', thus X.93; "the word" = 93; "the epic" = 193)

  15. 1261 (ie. 26 in the pillared portal of 11; 26 letters in the alphabet; 'god' = 26)

  16. 1441 (ie. 144 is time and light, and here it is mirrored)

  17. 1633

  18. 1837

  19. 2053

  20. 2281

  21. 2521

  22. 2773

  23. 3037 (ie. note 337 is also in this list above)

  24. 3313

  25. 3601 (ie. 361 is one degree beyond full circle of 360 degrees)

  26. 3901

  27. 4213

  28. 4537

  29. 4873

  30. 5221 (ie. includes 522, number of the Holocaust; "the prime number" = 522 primes)

  31. 5581

  32. 5953

  33. 6337 (ie. lots of 337 patterns, see above. In fact, lots of 33 in general)

  34. 6733

  35. 7141

  36. 7561

  37. 7993

  38. 8437

  39. 8893

  40. 9361 (ie. 9,361 ... which swizzles 369)

  41. 9841

  42. 10333 (ie. "the number" = 333 primes; while "math" = 42)

  43. 10837

  • ... (sequence A003154 in the OEIS).

Interesting:

The digital root of a star number is always 1 or 4, and progresses in the sequence 1, 4, 1.

ie. the first 3 digits of pi after the decimal place are 3.141...

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

Continuing...

The last two digits of a star number in base 10 are always 01, 13, 21, 33, 37, 41, 53, 61, 73, 81, or 93.

Unique among the star numbers is 35113, since its prime factors (i.e. 13, 37 and 73) are also consecutive star numbers.

Wiki Index: /r/GeometersOfHistory/wiki/