OFFSET
1,1
COMMENTS
The coefficient of first polynomial term with highest degree is always 1.
Each number in triangle is the sum of radicals of integers.
The absolute value of the entry in the k-th column is the k-th elementary symmetric function of the first n+(k-1) primes.
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
Fedor Igumnov, T(n,k) for n = 1..50
EXAMPLE
Triangle begins:
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\k | 1 2 3 4 5 6 7
n\ |
================================================
1 | -2;
2 | -5, 6;
3 | -10, 31, -30;
4 | -17, 101, -247, 210;
5 | -28, 288, -1358, 2927, -2310;
6 | -41, 652, -5102, 20581, -40361, 30030;
7 | -58,1349,-16186,107315,-390238,716167,-510510;
So equation x^7 -58*x^6 + 1349*x^5 -16186*x^4 + 107315*x^3 -390238*x^2+ 716167*x -510510 = 0 has 7 consecutive prime roots: 2,3,5,7,11,13,17
MAPLE
T:= n-> (p-> seq(coeff(p, x, n-i), i=1..n))(mul(x-ithprime(i), i=1..n)):
seq(T(n), n=1..10); # Alois P. Heinz, Aug 18 2019
MATHEMATICA
a = 1
For [i = 1, i < 10, i++,
a *= (x - Prime[i]);
Print[Drop[Reverse[CoefficientList[Expand[a], x]], 1]]
]
CROSSREFS
KEYWORD
AUTHOR
Fedor Igumnov, Feb 18 2014
EXTENSIONS
Name edited by Alois P. Heinz, Aug 18 2019
STATUS
approved