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A143121
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Triangle read by rows, T(n,k) = Sum_{j=k..n} prime(j), 1 <= k <= n.
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4
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2, 5, 3, 10, 8, 5, 17, 15, 12, 7, 28, 26, 23, 18, 11, 41, 39, 36, 31, 24, 13, 58, 56, 53, 48, 41, 30, 17, 77, 75, 72, 67, 60, 49, 36, 19, 100, 98, 95, 90, 83, 72, 59, 42, 23, 129, 127, 124, 119, 112, 101, 88, 71, 52, 29, 160, 158, 155, 150, 143, 132, 119, 102, 83, 60, 31
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OFFSET
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1,1
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COMMENTS
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Left border = A007504, sum of first n primes: (2, 5, 10, 27, 28, 41, ...).
Row sums = A014285: (2, 8, 23, 51, 106, 184, ...).
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LINKS
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FORMULA
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T(n,k) = Sum_{j=k..n} prime(j), 1 <= k <= n, primes = A000040.
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EXAMPLE
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First few rows of the triangle are:
2;
5, 3;
10, 8, 5;
17, 15, 12, 7;
28, 26, 23, 18, 11;
41, 39, 36, 31, 24, 13;
58, 56, 53, 48, 41, 30, 17;
...
T(5,3) = 23 = prime(3) + prime(4) + prime(5) = (5 + 7 + 11).
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MAPLE
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a:=proc(n, k) add(ithprime(j), j=k..n) end: seq(seq(a(n, k), k=1..n), n=1..11); # Muniru A Asiru, Oct 15 2018
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MATHEMATICA
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a[n_, k_] := a[n, k] = Plus@@Prime[Range[n - k + 1, n]]; Column[Table[a[n, k], {n, 15}, {k, n, 1, -1}], Center] (* Alonso del Arte, Jul 25 2011 *)
Table[Sum[Prime[j], {j, k, n}], {n, 1, 15}, {k, 1, n}]//Flatten (* G. C. Greubel, Oct 15 2018 *)
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PROG
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(Magma) [[(&+[NthPrime(j): j in [k..n]]): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Oct 15 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Corrected by Hanke Bremer, Nov 28 2008
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STATUS
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approved
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