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

0,2

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

References

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

Links

Table of n, a(n) for n=0..62.

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

Example

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.

Crossrefs

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

Sequence in context: A007951 A237590 A207336 * A190849 A277121 A325112

Adjacent sequences: A213536 A213537 A213538 * A213540 A213541 A213542

Keyword

nonn

Author

Kenneth Vollmar, Mar 03 2013

Extensions

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

Status

approved