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 A057062 Let R(i,j) be the infinite square array with antidiagonals 1; 2,3; 4,5,6; ...; the n-th prime is in antidiagonal a(n). 6
 2, 2, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The smallest integer in the j-th antidiagonal is A000124(j-1). So a(n) is the index j such that A000124(j-1) <= prime(n) < A000124(j). - R. J. Mathar, Dec 02 2011 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 FORMULA a(n) = round(sqrt(2*prime(n))). - Vladeta Jovovic, Jun 14 2003 EXAMPLE The array begins    1  3  6 10 15 ...    2  5  9 14 ...    4  8 13 ...    7 12 ...   11 ...   ... The third prime, 5, is in the 3rd antidiagonal, so a(3) = 3. MATHEMATICA Table[Round[Sqrt[2*Prime[n]]], {n, 100}] (* T. D. Noe, Dec 03 2011 *) PROG (PARI) a(n)=(sqrtint(8*prime(n))+1)\2 \\ Charles R Greathouse IV, Jul 26 2012 (Haskell) a057062 n = a057062_list !! (n-1) a057062_list = f 1 [1..] where    f j xs = (replicate (sum \$ map a010051 dia) j) ++ f (j + 1) xs'      where (dia, xs') = splitAt j xs -- Reinhard Zumkeller, Jul 26 2012 CROSSREFS Cf. A057045, A057048, A022846, A057057, A057054. A066888 counts how many times each positive integer appears in this sequence. Cf. A010051. Sequence in context: A305557 A099249 A050296 * A283993 A255572 A065855 Adjacent sequences:  A057059 A057060 A057061 * A057063 A057064 A057065 KEYWORD nonn AUTHOR Clark Kimberling, Jul 30 2000 STATUS approved

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Last modified December 14 05:36 EST 2019. Contains 329978 sequences. (Running on oeis4.)