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A213539 Variant of numbers for which there is at least one 3-smooth representation that is special of level k. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 17 09:00 EDT 2021. Contains 347478 sequences. (Running on oeis4.)