OFFSET
0,2
COMMENTS
All terms in A003592 are products T(n,k)*20^j, j >= 0.
When expressed in base 20, T(n,k) does not end in zero, yet 1/T(n,k) is a terminating fraction, regular to 20.
The first 5 terms are the proper divisors of 20.
For these reasons, the terms may be called vigesimal "proper regular" numbers.
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 = 0..5722
Eric Weisstein's World of Mathematics, Vigesimal
Wikipedia, Vigesimal
FORMULA
Row 0 contains the empty product, thus row length = 1.
Row n sorts {2^(2n-1), 5^n, 2^(2n), 2*5^n}, thus row length = 4.
EXAMPLE
Row 0 contains 1 since 1 is the empty product.
Row 1 contains 2, 4, 5, and 10 since these divide 20 and are not divisible by 20.
Row 2 contains 8, 16, 25, and 50 since these divide 20^2 but not 20. The other divisors of 20^2 either divide smaller powers of 20 or they are divisible by 20 and do not appear.
Row 3 contains 32, 64, 125, and 250 since these divide 20^3 but not 20^2. The other divisors of 20^3 either divide smaller powers of 20 or they are divisible by 20 therefore do not appear.
MATHEMATICA
{{1}}~Join~Array[Union@ Flatten@ {#, 2 #} &@ {2^(2 # - 1), 5^#} &, 11] // Flatten
CROSSREFS
KEYWORD
nonn,easy,base,tabf
AUTHOR
Michael De Vlieger, Apr 15 2022
STATUS
approved