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Zeisel Number


A number N=p_1p_2...p_n where the p_is are distinct primes and n>=3 such that

 p_i=Ap_(i-1)+B
(1)

for i=1, 2, ..., n, p_0 taken as 1, and with A and B some fixed integers. For example, 1885=1·5·13·29 is a Zeisel number with (A,B)=(2,3) since

 5=2·1+3;13=2·5+3;29=2·13+3,
(2)

as is 114985=1·5·13·29·61 since

 5=2·1+3;13=2·5+3;29=2·13+3;61=2·29+3.
(3)

The first few Zeisel numbers are 105, 1419, 1729, 1885, 4505, ... (OEIS A051015), which correspond to constants (1, 2), (4, -1), (1, 6), (2, 3), (3, 2), ....


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References

MathPages. "Zeisel Numbers." http://www.mathpages.com/home/kmath015.htm.Sloane, N. J. A. Sequence A051015 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Zeisel Number

Cite this as:

Weisstein, Eric W. "Zeisel Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ZeiselNumber.html

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