[math-fun] Fractions in primorial base
I calculated fractions in the primorial base. Consecutive places after the point represent the product of the first n primes, i.e. 1/2, 1/6, 1/30, 1/210, 1/2310, etc. I only go through the 15th prime, 47, so that every number will fit in 64 bits. Fractions with a square-free denominator all terminate. All other fractions do not. The expansion of 1/4 appears to be A102781. Other expansions (e.g. 1/8, 1/9, 1/25) aren't in OEIS. As usual, A through Z represent 10 through 35. When I ran off the end of the alphabet, I started over with the lowercase alphabet; a through z represent 36 through 61. Here are the first few integer reciprocals. For more fractions, and the code that generated them, see http://KeithLynch.net/primorial.txt 1/2: 0.1 1/3: 0.02 1/4: 0.01235689BEFIKLN... 1/5: 0.011 1/6: 0.01 1/7: 0.0042 1/8: 0.003529CE5LN9AAZ... 1/9: 0.003238B67JACDSV... 1/10: 0.003 1/11: 0.00251 1/12: 0.00235689BEFIKLN... 1/13: 0.002219 1/14: 0.0021 1/15: 0.002 1/16: 0.001614EGEAR4PQf... 1/17: 0.00153B8 1/18: 0.0014745CF9KOREF... 1/19: 0.0014078I 1/20: 0.00135689BEFIKLN...
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Keith F. Lynch