OFFSET
1,1
COMMENTS
From the left, the second column gives the sums of two consecutive primes, the third column gives the sums of three consecutive primes, etc. Thus, from the right, the rightmost column gives the running sum of all prime numbers up to that row.
LINKS
Michel Marcus, Table of n, a(n) for n = 1..5050 (first 100 rows)
FORMULA
T(n, k) = Sum_{i = n-k+1..n} prime(i), where prime(i) is the i-th prime number.
EXAMPLE
First few rows of triangle are:
2
3, 5
5, 8, 10
7, 12, 15, 17
11, 18, 23, 26, 28
...
T(5, 2) = 18 because the sum of the fourth and fifth primes (two consecutive primes) is 7 + 11 = 18.
T(5, 3) = 23 because the sum of the third, fourth and fifth primes (three consecutive primes) is 5 + 7 + 11 = 23.
MATHEMATICA
a[n_, k_] := a[n, k] = Plus@@Prime[Range[n - k + 1, n]]; Column[Table[a[n, k], {n, 15}, {k, n}], Center]
CROSSREFS
KEYWORD
AUTHOR
Alonso del Arte, Sep 07 2011
EXTENSIONS
More terms from Michel Marcus, Aug 31 2020
New name from David A. Corneth, Aug 31 2020
STATUS
approved