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A194939
Table T read by rows, where T(n, k) is the sum of the largest k primes up to and including prime(n), for 1 <= k <= n.
3
2, 3, 5, 5, 8, 10, 7, 12, 15, 17, 11, 18, 23, 26, 28, 13, 24, 31, 36, 39, 41, 17, 30, 41, 48, 53, 56, 58, 19, 36, 49, 60, 67, 72, 75, 77, 23, 42, 59, 72, 83, 90, 95, 98, 100, 29, 52, 71, 88, 101, 112, 119, 124, 127, 129, 31, 60, 83, 102, 119, 132, 143, 150, 155, 158, 160
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.
This triangle is the mirror image of A143121: left border are the primes (right border in the other one) while the right border is the sum of the first n primes (A007504, left border in the other one). Row sums are given by A014285, just like the other triangle.
On odd numbered rows, the central entry is exactly the same as the corresponding position in A143121: T(n, (n + 1)/2) = A143121(n, (n + 1)/2). The rest of the row is of course the reverse.
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
Cf. A143121 (rows reversed), A014285 (row sums).
Cf. A000040 (column k=1), A007504 (main diagonal).
Cf. A067377.
Sequence in context: A363058 A341122 A237825 * A135635 A238007 A204207
KEYWORD
nonn,easy,tabl
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