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Are there pentagonal numbers?

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882, 3015, 3151, 3290, 3432, 3577, 3725, 3876, 4030, 4187… (sequence A000326 in the OEIS).

What is the formula for hexagonal numbers?

No odd perfect numbers are known, hence all known perfect numbers are hexagonal. For example, the 2nd hexagonal number is 2×3 = 6; the 4th is 4×7 = 28; the 16th is 16×31 = 496; and the 64th is 64×127 = 8128. The largest number that cannot be written as a sum of at most four hexagonal numbers is 130.

What are the first four Heptagonal numbers?

The first few heptagonal numbers are: 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783, 874, 970, 1071, 1177, 1288, 1404, 1525, 1651, 1782, … (sequence A000566 in the OEIS)

Is 500 a Decagonal number?

0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326 (sequence A001107 in the OEIS)

What is the formula for Heptagonal number?

Heptagonal: \(P_{7,n}=n(5n-3)/2 \) with initial members 1, 7, 18, 34, 55, … Octagonal: \(P_{8,n}=n(3n-2) \) with initial members 1, 8, 21, 40, 65, … The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties: 1.

What is the definition of the Pentagon?

1 : the building in Washington, D.C., that is the headquarters of the U.S. Department of Defense. 2 : the leaders of the U.S. military There was disagreement between the President and the Pentagon over the new military budget.

How to find the formula for pentagonal numbers?

Since in the visual representation of \$p_n\$, the pentagon has \$n+1\$ dots on each side, counting the number of dots on each side and multiplying by \$5\$, we get, \$5(n+1)\$. However, we have counted the dots at the vertices twice, so we subtract \$5\$: which gives us \$p_n = 5n\$.

How is the n th pentagonal number p n defined?

The n th pentagonal number p n is defined algebraically as p n = n ( 3 n − 1) 2 for n ≥ 1. It can also be defined visually as the number of dots that can be arranged evenly in a pentagon

How are pentagonal numbers represented in programming language?

In general, a polygonal number (triangular number, square number, etc) is a number represented as dots or pebbles arranged in the shape of a regular polygon. The first few pentagonal numbers are: 1, 5, 12, etc. Below are the implementations of the above idea in different programming languages. // This code is contributed by vt_m.

How are generalized pentagonal numbers related to centered hexagonal numbers?

Generalized pentagonal numbers are closely related to centered hexagonal numbers. When the array corresponding to a centered hexagonal number is divided between its middle row and an adjacent row, it appears as the sum of two generalized pentagonal numbers, with the larger piece being a pentagonal number proper: