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A005145
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n copies of n-th prime.
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8
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2, 3, 3, 5, 5, 5, 7, 7, 7, 7, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31
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OFFSET
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1,1
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COMMENTS
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Seen as a square array read by antidiagonals, a subtable of the binary operation multiplication tables A297845, A306697 and A329329. - Peter Munn, Jan 15 2020
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REFERENCES
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Douglas Hofstadter, "Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought", Basic Books, 1995.
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LINKS
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FORMULA
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From Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 14 2006: (Start)
a(n) = prime(floor(1/2 + sqrt(2*n))).
When viewed as a square array A(n,k), the following hold for n >= 1, k >= 1:
A(n,k) = prime(n+k-1).
A(n,1) = A(1,n) = prime(n), where prime(n) = A000040(n).
A(n+1,k) = A(n,k+1) = A003961(A(n,k)).
A(n,k) = A297845(A(n,1), A(1,k)) = A306697(A(n,1), A(1,k)) = A329329(A(n,1), A(1,k)).
(End)
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EXAMPLE
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Triangle begins:
2;
3, 3;
5, 5, 5;
7, 7, 7, 7;
...
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MATHEMATICA
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Table[Prime[Floor[1/2 + Sqrt[2*n]]], {n, 1, 80}] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 14 2006 *)
Flatten[Table[Table[Prime[n], {n}], {n, 12}]] (* Alonso del Arte, Jan 18 2012 *)
Table[PadRight[{}, n, Prime[n]], {n, 15}]//Flatten (* Harvey P. Dale, Feb 29 2024 *)
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PROG
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(Haskell)
a005145 n k = a005145_tabl !! (n-1) !! (k-1)
a005145_row n = a005145_tabl !! (n-1)
a005145_tabl = zipWith ($) (map replicate [1..]) a000040_list
a005145_list = concat a005145_tabl
(Magma) [NthPrime(Round(Sqrt(2*n))): n in [1..60]]; // Vincenzo Librandi, Jan 18 2020
(Python)
from sympy import primerange
a = []; [a.extend([pn]*n) for n, pn in enumerate(primerange(1, 32), 1)]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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