## Friday, April 02, 2021

### [lckoyipy] decimal powers of 2

the decimal powers of 2 are a compactly expressible slow-growing exponential sequence:

2^0 = 1
2^0.1 = 1.071773
2^0.2 = 1.148
2^0.3 = 1.23
2^0.4 = 1.32
2^0.5 = 1.41
2^0.6 = 1.52
2^0.7 = 1.62
2^0.8 = 1.74
2^0.9 = 1.87
2^1 = 2

7.2% growth per year doubles in 10 years.

round to the nearest integer.  there are familiar waypoints at integer exponents.  for example:

2^9 = 512
2^9.1 = 549
2^9.2 = 588
2^9.3 = 630
2^9.4 = 676
2^9.5 = 724
2^9.6 = 776
2^9.7 = 832
2^9.8 = 891
2^9.9 = 955
2^10 = 1024
2^10.1 = 1097
2^10.2 = 1176
2^10.3 = 1261
2^10.4 = 1351
2^10.5 = 1448
2^10.6 = 1552
2^10.7 = 1663
2^10.8 = 1783
2^10.9 = 1911
2^11 = 2048
2^11.1 = 2195
2^11.2 = 2353
2^11.3 = 2521
2^11.4 = 2702
2^11.5 = 2896
2^11.6 = 3104
2^11.7 = 3327
2^11.8 = 3566
2^11.9 = 3822
2^12 = 4096

the range above is approximately the bit widths where integer factorization (future post) and integer discrete logarithms (future post: oreozfqr) become tough.

future post: decimal powers of 10.