First digits after the decimal point

Éric Angelini is not at the moment updating his latest sequence suggestion, so I will post my extension (assuming a 1, 2 start) here:

1, 2, 11, 5, 42, 4, 94, 7, 74, 20, 27, 129, 101, 777, 7618, 1124, 14753, 1218, 82554, 8156, 98795, 3206, 32451, 499, 15377, 2366, 15386, 1868, 121402, 2419, 199254, 5819, 292038, 9247, 316636, 13812, 43621, 38327, 36725, 95818, 260900, 20134, 771711, 58457, 54269, 92835, 60177, 55065, 91504, 25771, 281635, 53566, 190196, 355062, 1866812, 199551, 10689395, 186879, 17482653, 95960, 54888692, 216986, 39532004, 138119, 34938527, 829143, 23731481, 189726, 7994697, 1908167, 23867906, 7480187, 31339937, 11404557, 36389852, 32664599, 23949435, 5535335, 23112591, 6504115, 6357184, 3851878, 6059094, 489221, 807416, 1650409, 2044061, 12385171, 10283218, 83028464, 807417055, 82135674, 101726454, 26620507, 261687159, 61339564, 2344003581, 48771083, 2080674423, 22994000, ...

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