## Testing the Liliane sequence

This post had been private but since I did not have enough focus, it’s not over, but nevertheless I am sharing its content.

You can learn from my recent notes that I am also thinking about yet another sequence, i.e. the Liliane-k sequence – $f(n) = 3^{log_{\phi}{(k^{1/2}n+1/2)}}$.

Positions of $3^k$ in k-almost primes:
1, 2, 3, 5, 8, 14, 23, 39, 64, 103, 169, 269, 427, 676, 1065, 1669,
2628, 4104, 6414, 10023, 15608, 24281, 37733, 58503, 90616, 140187,
216625, 334527, 516126, 795632, 1225641, 1886570, 2901796, 4460359,
6851532, 10518476, 16138642, 24748319

Values of Liliane-5:
0, 9, 38, 90, 168, 273, 408, 573, 770, 1001, 1267, 1567, 1905, 2279,
2692, 3144, 3636, 4168, 4741, 5356, 6014, 6714, 7458, 8247, 9080,
9959, 10883, 11854, 12871, 13936, 15049