A213539 Variant of numbers for which there is at least one 3-smooth representation that is special of level k.

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 19, 20, 22, 23, 28, 29, 31, 32, 35, 37, 38, 40, 44, 46, 47, 49, 53, 56, 58, 62, 64, 65, 67, 70, 73, 74, 76, 79, 80, 85, 88, 89, 92, 94, 97, 98, 101, 103, 106, 112, 116, 119, 121, 124, 125, 128, 130, 131, 133, 134, 140, 143, 146

Offset: 0

Author

Kenneth Vollmar, Mar 03 2013

Keywords

• nonn

Comments

These numbers are of the form 3^k*2^{a_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 0 <= a_0 < a_1 < ... < a_k.

These values are those of sequence A116640 in addition to any multiple of two of elements of this sequence. - Kenneth Vollmar, Jun 05 2013

Examples

			n=19 has two 3-smooth representations that are special of level k. At k=1, 19 = 3^1*2^0 + 3^0*2^4. At k=2, 19 = 3^2*2^0 + 3^1*2^1 + 3^0*2^2.
		

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. A116623, A116640, A116641, A119733, A226383, A003586.

Extensions

Corrected a reference to another sequence and added cross references - Joe Slater, Dec 19 2016