A353384 Irregular triangle T(n,k) with row n listing A003592(j) not divisible by 20 such that A352218(A003592(j)) = n.
1, 2, 4, 5, 10, 8, 16, 25, 50, 32, 64, 125, 250, 128, 256, 625, 1250, 512, 1024, 3125, 6250, 2048, 4096, 15625, 31250, 8192, 16384, 78125, 156250, 32768, 65536, 390625, 781250, 131072, 262144, 1953125, 3906250, 524288, 1048576, 9765625, 19531250, 2097152, 4194304, 48828125, 97656250
Offset: 0
Examples
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.
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
Programs
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Mathematica
{{1}}~Join~Array[Union@ Flatten@ {#, 2 #} &@ {2^(2 # - 1), 5^#} &, 11] // Flatten
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.
Comments