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Revision History for A359321

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a(n) is the smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists.
(history; published version)

#4 by N. J. A. Sloane at Sat Dec 31 15:25:39 EST 2022

STATUS

proposed

approved

#3 by Ilya Gutkovskiy at Sun Dec 25 17:46:33 EST 2022

STATUS

editing

proposed

Discussion

Fri Dec 30

12:08

David A. Corneth: I get a(3) = 305. For n = 3, 305 = 1+ 84 + 220 = 20 + 120 + 165 = 56 + 84 + 165. What do I do wrong?

14:33

David A. Corneth: Okay 305 isn't 3-gonal. a(7) > 10^5. the number of ways is > 7 for 19172 < k < 100000.

14:41

David A. Corneth: similar issues for a(8). Now 22554 < k <= 100000.

#2 by Ilya Gutkovskiy at Sun Dec 25 17:19:37 EST 2022

NAME

allocated for Ilya Gutkovskiya(n) is the smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists.

DATA

2300, 6201, 8125, 6391

OFFSET

3,1

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>

EXAMPLE

For n = 3: 2300 = 1 + 969 + 1330 = 56 + 220 + 2024 = 165 + 364 + 1771.

For n = 4: 6201 = 1 + 91 + 1785 + 4324 = 1 + 285 + 1015 + 4900 = 30 + 140 + 506 + 5525 = 91 + 819 + 1496 + 3795.

CROSSREFS

Cf. A080851, A350210, A350397, A350423.

KEYWORD

allocated

nonn,more

AUTHOR

Ilya Gutkovskiy, Dec 25 2022

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Sun Dec 25 17:19:37 EST 2022

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved