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Message: [QUOTE="Phrogz, post: 4525247"] Interestingly, there doesn't seem to be a pattern as to the number of happy numbers in a given range as the base changes: (My results...might be wrong. :) How many Happy numbers between 1..10000? Base 2: 10000 happy numbers. Base 3: 1988 happy numbers. Base 4: 10000 happy numbers. Base 5: 2571 happy numbers. Base 6: 645 happy numbers. Base 7: 162 happy numbers. Base 8: 549 happy numbers. Base 9: 627 happy numbers. Base 10: 1442 happy numbers. Base 11: 196 happy numbers. Base 12: 24 happy numbers. Base 13: 582 happy numbers. Base 14: 93 happy numbers. Base 15: 164 happy numbers. Base 16: 2585 happy numbers. Base 17: 253 happy numbers. Base 18: 4154 happy numbers. Base 19: 3647 happy numbers. Base 20: 1616 happy numbers. Base 21: 45 happy numbers. Base 22: 17 happy numbers. Base 23: 19 happy numbers. Base 24: 9 happy numbers. Base 25: 519 happy numbers. Base 26: 377 happy numbers. Base 27: 279 happy numbers. Base 28: 6 happy numbers. Base 29: 1730 happy numbers. Base 30: 5266 happy numbers. Base 31: 11 happy numbers. Base 32: 11 happy numbers. Base 33: 84 happy numbers. Base 34: 192 happy numbers. Base 35: 77 happy numbers. Base 36: 50 happy numbers. [/QUOTE]