Difference between revisions 4143264 and 4186841 on enwiki

A '''Zeisel number''' is a [[square-free]] integer ''k'' with at least three prime factors that when plugged into the equation <math>2^{k - 1} + k</math> yeields a [[prime number]]. Also, all the prime factors of ''k''must fall into the pattern <math>p_x = ap_{x - 1} + b</math> where ''a'' and ''b'' are fixed constants and ''x'' is the index number of each prime factor in the factorization, sorted from highlowest to lowhighest. fFor the purpose of determining Zeisel numbers, <math>p_0 = 1</math>. The first few Zeisel numbers are

[[105 (number)|105]], [[1419 (number)|1419]], [[1729 (number)|1729]], 1885, 4505, 5719, 15387, 24211, 25085, 27559, 31929, 54205, 59081, 114985, 207177, 208681, 233569, 287979, 294409, 336611, 353977, 448585, 507579, 982513, 1012121, 1073305, 1242709, 1485609, 2089257, 2263811, 2953711

To give an example, 1729 is a Zeisel number with the constants ''a'' = 1 and ''b'' = 6, it's factors being 7, 13 and 19, falling into the pattern

<math>p_1 = 7, p_1 = 1p_0 + 6</math>
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<math>p_2 = 13, p_2 = 1p_1 + 6</math>
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<math>p_3 = 19, p_3 = 1p_2 + 6</math>

These kind of numbers were first studied by the aAustrian? mathematician [[Helmut Zeisel]].

==Ext.ernal Resources==

*[http://www.research.att.com/projects/OEIS?Anum=A051015 Sloane sSeq auence A051015]
*[http://mathworld.wolfram.com/ZeiselNumber.html MathWorld article]
*[http://www.mathpages.com/home/kmath015.htm MathPages article]