***** SPOILER SPACE ***** 14 121 15 125 16 128 17 144 18 169 19 196 20 216 21 225 22 243 23 256 24 289 25 324 26 343 27 361 28 400 29 441 30 484 31 512 32 529 33 576 34 625 ... 1086 952576 1087 954529 1088 956484 1089 958441 1090 960400 1091 962361 1092 964324 1093 966289 1094 968256 1095 970225 1096 970299 1097 972196 1098 974169 1099 976144 1100 978121 1101 980100 1102 982081 1103 984064 1104 986049 1105 988036 1106 990025 ***** SPOILER SPACE ***** On Jun 8, 2014, at 12:59 PM, rcs@xmission.com wrote:
Puzzle: In my preferred date notation, today is 140608. It's also Cube Day, in fact 52^3. When's the next Cube Day? When was the previous Cube Day? When is the next Power Day?
Letting the year range from 00 to 99, the month from 01 to 12, and the day from 01 to 31, we drop leading zeros and compare to the 1093 terms of A001597 (perfect powers, the exponent assumed to be greater than 1) within our possible range (101-991231). There are 62 hits: {0,0} {0,1} {2,1} = 11^2 {0,0} {0,1} {2,5} = 5^3 {0,0} {0,1} {2,8} = 2^7 {0,0} {0,2} {1,6} = 6^3 {0,0} {0,2} {2,5} = 15^2 {0,0} {0,3} {2,4} = 18^2 {0,0} {0,5} {1,2} = 8^3 {0,0} {0,5} {2,9} = 23^2 {0,0} {0,6} {2,5} = 25^2 {0,0} {0,7} {2,9} = 9^3 {0,0} {1,0} {2,4} = 32^2 {0,0} {1,2} {2,5} = 35^2 {0,1} {0,2} {0,1} = 101^2 {0,1} {0,4} {0,4} = 102^2 {0,1} {0,6} {0,9} = 103^2 {0,1} {0,8} {1,6} = 104^2 {0,1} {1,0} {2,5} = 105^2 {0,2} {1,0} {2,5} = 145^2 {0,3} {0,6} {2,5} = 175^2 {0,4} {0,4} {0,1} = 201^2 {0,4} {0,8} {0,4} = 202^2 {0,4} {1,2} {0,9} = 203^2 {0,5} {0,6} {2,5} = 225^2 {0,6} {0,5} {1,6} = 246^2 {0,6} {1,0} {0,9} = 247^2 {0,7} {0,2} {2,5} = 265^2 {0,8} {1,2} {2,5} = 285^2 {0,9} {0,6} {0,1} = 301^2 {0,9} {1,1} {2,5} = 45^3 {0,9} {1,2} {0,4} = 302^2 {1,0} {1,1} {2,4} = 318^2 {1,1} {0,2} {2,4} = 332^2 {1,2} {0,4} {0,9} = 347^2 {1,2} {1,1} {0,4} = 348^2 {1,3} {0,3} {2,1} = 361^2 {1,4} {0,6} {0,8} = 52^3 TODAY {1,4} {0,6} {2,5} = 375^2 {1,6} {0,8} {0,1} = 401^2 {1,8} {0,6} {2,5} = 425^2 {2,0} {0,7} {0,4} = 448^2 {2,5} {1,0} {0,1} = 501^2 {2,6} {1,1} {2,1} = 511^2 {2,9} {0,5} {2,1} = 539^2 {3,0} {0,3} {0,4} = 548^2 {3,3} {0,6} {2,5} = 575^2 {3,6} {1,2} {0,1} = 601^2 {3,9} {0,6} {2,5} = 625^2 {4,2} {1,2} {0,1} = 649^2 {5,1} {1,2} {2,5} = 715^2 {5,4} {0,2} {2,5} = 735^2 {5,6} {1,0} {0,1} = 749^2 {6,0} {0,6} {2,5} = 775^2 {6,8} {0,6} {2,5} = 825^2 {7,2} {0,8} {0,1} = 849^2 {7,3} {1,0} {2,5} = 855^2 {7,9} {0,3} {2,1} = 889^2 {8,0} {1,0} {2,5} = 895^2 {9,0} {0,6} {0,1} = 949^2 {9,1} {0,1} {1,6} = 954^2 {9,3} {1,2} {2,5} = 965^2 {9,5} {0,6} {2,5} = 975^2 {9,7} {0,2} {2,5} = 985^2 TODAY is marked. The chart is cyclical, so the next Cube Day will be 25 Jan 3000. The previous Cube Day was 25 Nov 2009. The next Power Day is 25 Jun 2014.