Linearizing an LED for 800 pwm steps'?

[HankMcSpank]

but the numbers are non linear ...for example here are the first 256 numbers....

0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,
8,8,8,8,8,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,
14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,17,17,17,17,17,18,18,18,18,18,19,19,19,
19,19,20,20,20,20,20,21,21,21,21,22,22,22,22,22,23,23,23,23,23,24,24,24,24,24,25,25,25,
25,26,26,26,26,26,27,27,27,27,28,28,28,28,28,29,29,29,29,30,30,30,30,31,31,31,31,31,32,
32,32,32,33,33,33,33,34,34,34,34,35,35,35,35,36,36,36,36,37,37,37,37,38,38,38,38,39,39,39,
39,40,40,40,40,41,41,41,41,42,42,42,43,43,43,43,44,44,44,44,45,45,45,46,46,46,46,47,47,47,
48,48,48,48,49,49,49,50,50,50,50,51,51,51,52,52,52,53,53,53,53,54,54,54,55,55,55,56,56,56,57

& here are the final 256 values I need to look up against...

57,57,58,58,58,59,59,59,59,60,60,60,61,61,62,62,62,63,63,63,64,64,64,65,65,65,66,66,66,67,
67,67,68,68,69,69,69,70,70,70,71,71,72,72,72,73,73,74,74,74,75,75,76,76,76,77,77,78,78,78,
79,79,80,80,80,81,81,82,82,83,83,84,84,84,85,85,86,86,87,87,88,88,89,89,90,90,90,91,91,92,
92,93,93,94,94,95,95,96,96,97,98,98,99,99,100,100,101,101,102,102,103,104,104,105,105,106,
106,107,108,108,109,109,110,111,111,112,113,113,114,114,115,116,116,117,118,118,119,120,
120,121,122,123,123,124,125,125,126,127,128,128,129,130,131,132,132,133,134,135,136,137,
137,138,139,140,141,142,143,144,145,145,146,147,148,149,150,151,152,153,154,155,157,158,
159,160,161,162,163,164,166,167,168,169,171,172,173,175,176,177,179,180,182,183,185,186,188,
189,191,193,194,196,198,200,201,203,205,207,209,211,213,216,218,220,223,225,228,230,233,236,
239,241,245,248,251,255,258,262,266,270,275,279,284,290,295,301,308,315,323,332,341,352,365,
380,398,422,455,512

(so the second tranche are mainly bytes, but a fair few words too)


I don't see how maths can be applied to the numbers like you're suggesting?

here's the vibe I'm try to get (ie the data above plotted on a graph)...