The First 1500 Hamming Numbers

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 21870 22500 23040 23328 24000 24300 24576 25000 25600 25920 26244 27000 27648 28125 28800 29160 30000 30375 30720 31104 31250 32000 32400 32768 32805 33750 34560 34992 36000 36450 36864 37500 38400 38880 39366 40000 40500 40960 41472 43200 43740 45000 46080 46656 46875 48000 48600 49152 50000 50625 51200 51840 52488 54000 54675 55296 56250 57600 58320 59049 60000 60750 61440 62208 62500 64000 64800 65536 65610 67500 69120 69984 72000 72900 73728 75000 76800 77760 78125 78732 80000 81000 81920 82944 84375 86400 87480 90000 91125 92160 93312 93750 96000 97200 98304 98415 100000 101250 102400 103680 104976 108000 109350 110592 112500 115200 116640 118098 120000 121500 122880 124416 125000 128000 129600 131072 131220 135000 138240 139968 140625 144000 145800 147456 150000 151875 153600 155520 156250 157464 160000 162000 163840 164025 165888 168750 172800 174960 177147 180000 182250 184320 186624 187500 192000 194400 196608 196830 200000 202500 204800 207360 209952 216000 218700 221184 225000 230400 233280 234375 236196 240000 243000 245760 248832 250000 253125 256000 259200 262144 262440 270000 273375 276480 279936 281250 288000 291600 294912 295245 300000 303750 307200 311040 312500 314928 320000 324000 327680 328050 331776 337500 345600 349920 354294 360000 364500 368640 373248 375000 384000 388800 390625 393216 393660 400000 405000 409600 414720 419904 421875 432000 437400 442368 450000 455625 460800 466560 468750 472392 480000 486000 491520 492075 497664 500000 506250 512000 518400 524288 524880 531441 540000 546750 552960 559872 562500 576000 583200 589824 590490 600000 607500 614400 622080 625000 629856 640000 648000 655360 656100 663552 675000 691200 699840 703125 708588 720000 729000 737280 746496 750000 759375 768000 777600 781250 786432 787320 800000 810000 819200 820125 829440 839808 843750 864000 874800 884736 885735 900000 911250 921600 933120 937500 944784 960000 972000 983040 984150 995328 1000000 1012500 1024000 1036800 1048576 1049760 1062882 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