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.

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