A226383 Numbers for which there is at least one 3-smooth representation that is special of level k.

5, 7, 11, 19, 19, 23, 29, 31, 35, 37, 47, 49, 53, 65, 65, 67, 73, 79, 85, 85, 89, 89, 97, 101, 103, 119, 121, 121, 125, 131, 133, 143, 143, 149, 151, 157, 161, 169, 175, 179, 185, 185, 197, 205, 211, 211, 215, 221, 223, 227, 233, 239, 251, 259, 259, 259, 269, 271, 275, 277, 283, 287, 287, 289, 313, 313, 319, 323, 323

Offset: 0

Author

Kenneth Vollmar, Jun 05 2013

Keywords

• nonn

Comments

These numbers are of the form 3^k*2^0 + 3^{k-1}*2^{a_1} + ... + 3^1*2^{a_{k-1}} + 3^0*2^{a_k} in which every power 3^i appears, 0 <= i <= k, and where a_i satisfies a_0 = 0, a_0 < a_1 < ... < a_k.

References

• Kenneth Vollmar, Recursive calculation of 3-smooth representations special of level k, To be submitted mid-2013.

Links

• R. Blecksmith, M. McCallum and J. L. Selfridge, 3-smooth representations of integers, Amer. Math. Monthly, 105 (1998), 529-543.

Crossrefs

Cf. A213539, A003586.