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%I #38 Dec 22 2016 02:46:02
%S 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,
%T 15,15,15,16,16,17,17,17,17,18,18,18,19,19,19,20,20,20,20,21,21,21,21,
%U 22,22,22,22,23,23,23,23,24,24,24,24,25,25
%N 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).
%C 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
%H T. D. Noe, <a href="/A057062/b057062.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = round(sqrt(2*prime(n))). - _Vladeta Jovovic_, Jun 14 2003
%e The array begins
%e 1 3 6 10 15 ...
%e 2 5 9 14 ...
%e 4 8 13 ...
%e 7 12 ...
%e 11 ...
%e ...
%e The third prime, 5, is in the 3rd antidiagonal, so a(3) = 3.
%t Table[Round[Sqrt[2*Prime[n]]], {n, 100}] (* _T. D. Noe_, Dec 03 2011 *)
%o (PARI) a(n)=(sqrtint(8*prime(n))+1)\2 \\ _Charles R Greathouse IV_, Jul 26 2012
%o (Haskell)
%o a057062 n = a057062_list !! (n-1)
%o a057062_list = f 1 [1..] where
%o f j xs = (replicate (sum $ map a010051 dia) j) ++ f (j + 1) xs'
%o where (dia, xs') = splitAt j xs
%o -- _Reinhard Zumkeller_, Jul 26 2012
%Y Cf. A057045, A057048, A022846, A057057, A057054. A066888 counts how many times each positive integer appears in this sequence.
%Y Cf. A010051.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jul 30 2000
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