A099535 Sum of the first n decimal places of log(2).
6, 15, 18, 19, 23, 30, 31, 39, 39, 44, 49, 58, 67, 71, 76, 79, 79, 88, 92, 93, 100, 102, 105, 107, 108, 110, 111, 115, 120, 128, 129, 136, 142, 147, 153, 161, 161, 168, 173, 178, 178, 178, 179, 182, 186, 189, 195, 195, 197, 202, 207, 209, 214, 218, 219, 221, 221
Offset: 1
Examples
log(2) decimals = 693147180559945... so the sums are 6, 6+9, 6+9+3, 6+9+3+1,... which are 6, 15, 18, 19, ...
Programs
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Mathematica
Accumulate[RealDigits[Log[2],10,100][[1]]] (* Harvey P. Dale, Mar 23 2011 *)