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A143121
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Triangle read by rows, T(n,k) = sum {j=k..n} p(j), 1<=k<=n.
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1
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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, 39, 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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Left border = A007504, sum of first n primes: (2, 5, 10, 27, 28, 41,...).
Right border = primes, A000040.
Row sums = A014285: (2, 8, 23, 51, 106, 184,...).
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FORMULA
| Triangle read by rows, T(n,k) = sum {j=k..n} p(j), 1<=k<=n, primes = A000040. = A000012 * (A000040 * 0^(n-k)) * A000012.
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EXAMPLE
| 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 = p(3) + p(4) + p(5) = (5 + 7 + 11).
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MATHEMATICA
| 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] (* From Alonso del Arte, Jul 25 2011 *)
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PROG
| (PARI) a(n, k)=my(s); forprime(p=prime(k), prime(n), s+=p); s \\ Charles R Greathouse IV, Jul 25 2011
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CROSSREFS
| Cf. A000040, A007504, A014285.
Sequence in context: A064664 A078386 A163254 * A101492 A138765 A097753
Adjacent sequences: A143118 A143119 A143120 * A143122 A143123 A143124
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Jul 26 2008
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EXTENSIONS
| Corrected by Hanke Bremer, Nov 28 2008
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