A352218 a(n) = least k such that A003592(n) | 20^k.

0, 1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 2, 3, 2, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 5, 4, 4, 3, 3, 5, 4, 4, 3, 3, 6, 4, 5, 5, 4, 3, 6, 4, 5, 5, 4, 3, 7, 4, 6, 5, 5, 6, 4, 7, 4, 6, 5, 5, 6, 4, 8, 4, 7, 5, 6, 6, 5, 8, 7, 4, 7, 5, 6, 6, 5, 9, 7, 4, 8, 5, 7, 6, 6, 9, 7, 5, 8

Offset: 1

Author

Michael De Vlieger, Mar 08 2022

Keywords

• nonn
• easy
• base

Comments

Also, number of digits in the vigesimal (base 20) expansion of terminating unit fractions 1/A003592.

Examples

			a(1) = 0 since A003592(1) = 1 | 20^0.
a(4) = 1 since A003592(4) = 5 | 20^1; 1/5 in base 20 = 0.4.
a(5) = 2 since A003592(5) = 8 | 20^2; 1/8 in base 20 = 0.2a, where "a" is digit 10, etc.
		

References

• G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Chapter IX: The Representation of Numbers by Decimals, Theorem 136. 8th ed., Oxford Univ. Press, 2008, 144-145.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10212 (A003592(10212) = 20^50)
• Eric Weisstein's World of Mathematics, Vigesimal.
• Wikipedia, Vigesimal.

Crossrefs

Cf. A003592, A086415, A117920.

Programs

Mathematica

With[{nn = 360000}, Sort[Join @@ Table[{2^a*5^b, Max[Ceiling[a/2], b]}, {a, 0, Log2[nn]}, {b, 0, Log[5, nn/(2^a)]}]][[All, -1]] ]