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 A005145 n copies of n-th prime. 8
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Seen as a triangle read by rows: T(n,k) = A000040(n), 1 <= k <= n; row sums = A033286; central terms = A031368. - Reinhard Zumkeller, Aug 05 2009 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 REFERENCES Douglas Hofstadter, "Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought", Basic Books, 1995. LINKS Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened FORMULA From Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 14 2006: (Start) a(n) = prime(floor(1/2 + sqrt(2*n))). a(n) = A000040(A002024(n)). (End) From Peter Munn, Jan 15 2020: (Start) 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) Sum_{n>=1} 1/a(n)^2 = A097906. - Amiram Eldar, Aug 16 2022 EXAMPLE Triangle begins: 2; 3, 3; 5, 5, 5; 7, 7, 7, 7; ... MATHEMATICA 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 *) PROG (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 -- Reinhard Zumkeller, Jul 12 2014, Mar 18 2011, Oct 17 2010 (PARI) a(n) = prime(round(sqrt(2*n))) \\ Charles R Greathouse IV, Oct 23 2015 (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)] print(a) # Michael S. Branicky, Jul 13 2022 CROSSREFS Sequences with similar definitions: A002024, A175944. Cf. A000040 (range of values), A003961, A031368 (main diagonal), A033286 (row sums), A097906. Subtable of A297845, A306697, A329329. Sequence in context: A053046 A261179 A066658 * A280740 A156350 A076367 Adjacent sequences: A005142 A005143 A005144 * A005146 A005147 A005148 KEYWORD nonn,nice,tabl AUTHOR STATUS approved

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Last modified December 5 04:50 EST 2022. Contains 358578 sequences. (Running on oeis4.)