I haven’t had a chance to post anything here since the beginning of last semester. I’m in a class at the moment where all of the programming assignments involves annoying little math algorithms. The most recent required us to generate the first N hamming numbers using an efficient algorithm that involved a single for-loop. Now, the homework hasn’t actually been posted yet, so I’m not going to put the code out here. But, while I was testing my solution, I searched on google for a list of Hamming Numbers. I had a lot of trouble finding anything more than the first ten, twenty, or thirty.
So, for anyone who needs to know what the first 1000 hamming numbers are, you have come to the right place.
First, what is a Hamming Number? A Hamming Number is an element of the Hamming Set H={2^I*3^j*5^k|I,j,k >= 0}. Hamming Numbers are a type of Smooth Numbers.
The first 1500 Hamming Numbers are listed below–I couldn’t generate anymore numbers than this without the JVM running out of memory. It took my laptop ~260ms to generate this list.
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54 60 64 72 75 80 81 90 96 100 108 120 125 128 135 144 150 160 162 180 192 200 216 225 240 243 250 256 270 288 300 320 324 360 375 384 400 405 432 450 480 486 500 512 540 576 600 625 640 648 675 720 729 750 768 800 810 864 900 960 972 1000 1024 1080 1125 1152 1200 1215 1250 1280 1296 1350 1440 1458 1500 1536 1600 1620 1728 1800 1875 1920 1944 2000 2025 2048 2160 2187 2250 2304 2400 2430 2500 2560 2592 2700 2880 2916 3000 3072 3125 3200 3240 3375 3456 3600 3645 3750 3840 3888 4000 4050 4096 4320 4374 4500 4608 4800 4860 5000 5120 5184 5400 5625 5760 5832 6000 6075 6144 6250 6400 6480 6561 6750 6912 7200 7290 7500 7680 7776 8000 8100 8192 8640 8748 9000 9216 9375 9600 9720 10000 10125 10240 10368 10800 10935 11250 11520 11664 12000 12150 12288 12500 12800 12960 13122 13500 13824 14400 14580 15000 15360 15552 15625 16000 16200 16384 16875 17280 17496 18000 18225 18432 18750 19200 19440 19683 20000 20250 20480 20736 21600 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