The record today is N(3003)=8. In addition there are 6 sporadic cases N(120)=N(210)=N(1540)=N(7140)=N(11628)=N(24310)=6 and a infinite parametric family p(t)=C(n,k-1)=C(n-1,k)⇒N(p(t))≥6, p(1)=1 and p(2)=3003, although no other case is known with N(p(t))>6.
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p(t)=C(n(t),k(t)-1)=C(n(t-1),k(t) for n(t)=(5u(4t)+v(4t)-2)/10 k(t)=(5u(4t)-v(4t)+2)/10 being u(t) and v(t) the t-th number of Fibonacci and Lucas respectivaly. p(1)=1 p(2)=3003 p(3)=61218182743304701891431482520 p(4)=3.5·10²⁰⁴ p(5)=4.5·10¹⁴¹¹ A infinity but low dense family
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Not counting the value of 1, of course.
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The image literally includes the line "N(1) = ∞"
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Ankhset of Thebes (894-837 BCE) attempted to build a ziggurat using these numbers to please the god Anubis. He completed the lowest four layers before the annual Nile flood destroyed his handiwork. Unflustered, he exclaimed, “A dog ate my homework!!”
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Wow = My Mentor Professor Dr David Singmaster from the USA !
@xiaolon73722402 and@gabrielanthonyp .@nasa@esa .
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Is there any number A such that N(A)=5? No one knows!!!!!
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The Triangle is symetrical, so no. A number 1< either occurs twice or four times.
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One of my absolute favorite problems.
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