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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.

%I A194939 #36 Dec 15 2022 21:24:30
%S A194939 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,
%T A194939 53,56,58,19,36,49,60,67,72,75,77,23,42,59,72,83,90,95,98,100,29,52,
%U A194939 71,88,101,112,119,124,127,129,31,60,83,102,119,132,143,150,155,158,160
%N 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.
%C A194939 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.
%C A194939 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.
%C A194939 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.
%H A194939 Michel Marcus, <a href="/A194939/b194939.txt">Table of n, a(n) for n = 1..5050</a> (first 100 rows)
%F A194939 T(n, k) = Sum_{i = n-k+1..n} prime(i), where prime(i) is the i-th prime number.
%e A194939 First few rows of triangle are:
%e A194939 2
%e A194939 3,   5
%e A194939 5,   8, 10
%e A194939 7,  12, 15, 17
%e A194939 11, 18, 23, 26, 28
%e A194939 ...
%e A194939 T(5, 2) = 18 because the sum of the fourth and fifth primes (two consecutive primes) is 7 + 11 = 18.
%e A194939 T(5, 3) = 23 because the sum of the third, fourth and fifth primes (three consecutive primes) is 5 + 7 + 11 = 23.
%t A194939 a[n_, k_] := a[n, k] = Plus@@Prime[Range[n - k + 1, n]]; Column[Table[a[n, k], {n, 15}, {k, n}], Center]
%Y A194939 Cf. A143121 (rows reversed), A014285 (row sums).
%Y A194939 Cf. A000040 (column k=1), A007504 (main diagonal).
%Y A194939 Cf. A067377.
%K A194939 nonn,easy,tabl
%O A194939 1,1
%A A194939 _Alonso del Arte_, Sep 07 2011
%E A194939 More terms from _Michel Marcus_, Aug 31 2020
%E A194939 New name from _David A. Corneth_, Aug 31 2020