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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: A136378 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 November 22 09:35 EST 2017. Contains 295076 sequences.