Talk:Hamming numbers: Difference between revisions

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:::: So I think it is safe to say that we agree on the value of the 1690th Hamming number. Here it doesn't matter wheter indexing is zero-based or one-based. If we agree that the first Hamming number is 1, it is clear what we mean by the 1690th Hamming number. The only difference between zero-based indexing compared to one-based is that the first Hamming number is called hamming(0) in the former case and hamming(1) in the latter. Similarly for the 1690th Hamming number: with zero-based indexing it is called hamming(1689) as compared to hamming(1690) with one-based indexing. Anyway, to me it still looks like the last Hamming number before 2^31 is the 1691th, since the 1692th Hamming number is equal to 2^31. --[[User:Dsnouck|Dsnouck]] 10:48, 3 December 2009 (UTC)

::::: Hence the error is in the task itself. But it's not serious; any implementation that can compute one ought to be able to do the other (and if it can't... well, that's pretty poor). Doing the millionth though, that takes a bit more computation. Especially given that it has 84 digits in decimal notation. –[[User:Dkf|Donal Fellows]] 11:15, 3 December 2009 (UTC)

Calculations using the Python implementation give:

<lang python>>>> # Create a zero-based list of the Hamming numbers

>>> h = list(islice(raymonds_hamming(), 1695))

>>> # Show some of the vaules in one-based, (as well as zero based) indexing

>>> for i in chain(range(20), range(1689,1693)):

print "(i=%4i), n=%4i, h(n)=%10i, (h(n)<2**31) = %s" % (i, i+1, h[i], h[i]<2**31)

(i= 0), n= 1, h(n)= 1, (h(n)<2**31) = True

(i= 1), n= 2, h(n)= 2, (h(n)<2**31) = True

(i= 2), n= 3, h(n)= 3, (h(n)<2**31) = True

(i= 3), n= 4, h(n)= 4, (h(n)<2**31) = True

(i= 4), n= 5, h(n)= 5, (h(n)<2**31) = True

(i= 5), n= 6, h(n)= 6, (h(n)<2**31) = True

(i= 6), n= 7, h(n)= 8, (h(n)<2**31) = True

(i= 7), n= 8, h(n)= 9, (h(n)<2**31) = True

(i= 8), n= 9, h(n)= 10, (h(n)<2**31) = True

(i= 9), n= 10, h(n)= 12, (h(n)<2**31) = True

(i= 10), n= 11, h(n)= 15, (h(n)<2**31) = True

(i= 11), n= 12, h(n)= 16, (h(n)<2**31) = True

(i= 12), n= 13, h(n)= 18, (h(n)<2**31) = True

(i= 13), n= 14, h(n)= 20, (h(n)<2**31) = True

(i= 14), n= 15, h(n)= 24, (h(n)<2**31) = True

(i= 15), n= 16, h(n)= 25, (h(n)<2**31) = True

(i= 16), n= 17, h(n)= 27, (h(n)<2**31) = True

(i= 17), n= 18, h(n)= 30, (h(n)<2**31) = True

(i= 18), n= 19, h(n)= 32, (h(n)<2**31) = True

(i= 19), n= 20, h(n)= 36, (h(n)<2**31) = True

(i=1689), n=1690, h(n)=2123366400, (h(n)<2**31) = True

(i=1690), n=1691, h(n)=2125764000, (h(n)<2**31) = True

(i=1691), n=1692, h(n)=2147483648, (h(n)<2**31) = False

(i=1692), n=1693, h(n)=2149908480, (h(n)<2**31) = False</lang>

Since we are using 1 based indices for h(n) then the task should use '''1691'''. --[[User:Paddy3118|Paddy3118]] 16:39, 3 December 2009 (UTC)