A064924 If n is prime then a(n) = n; for the subsequent nonprime positions a(n + k) = (k+1)*n; then at the next prime position a new subsequence begins.

2, 3, 6, 5, 10, 7, 14, 21, 28, 11, 22, 13, 26, 39, 52, 17, 34, 19, 38, 57, 76, 23, 46, 69, 92, 115, 138, 29, 58, 31, 62, 93, 124, 155, 186, 37, 74, 111, 148, 41, 82, 43, 86, 129, 172, 47, 94, 141, 188, 235, 282, 53, 106, 159, 212, 265, 318, 59, 118, 61, 122, 183, 244

Offset: 2

Author

Reinhard Zumkeller, Oct 14 2001

Keywords

• nice
• nonn
• look

Comments

A064920(a(n)) = n.

Examples

			a(7) = A007917(7) * (A064722(7) + 1) = 7 * (0 + 1) = 7; a(8) = A007917(8) * (A064722(8) + 1) = 7 * (1 + 1) = 14; a(9) = A007917(9) * (A064722(9) + 1) = 7 * (2 + 1) = 21; a(10) = A007917(10) * (A064722(10) + 1) = 7 * (3 + 1) = 28; a(11) = 11.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A064920, A064923, A007917, A064722, A064919.

Programs

Haskell

import Data.List (genericTake)
a064924 n = a064924_list !! (n-1)
a064924_list = concat $ zipWith (\p g -> genericTake g [p, 2 * p ..])
   a000040_list $ zipWith (-) (tail a000040_list) a000040_list
-- Reinhard Zumkeller, Jul 05 2013

Mathematica

a[n_?PrimeQ] := n; a[n_] := NextPrime[n, -1]*(n - NextPrime[n, -1] + 1); Table[a[n], {n, 2, 64}] (* Jean-François Alcover, Sep 19 2011 *)
Flatten[First[#]Range[Last[#]-First[#]]&/@Partition[Prime[Range[20]],2,1]] (* Harvey P. Dale, May 03 2012 *)

PARI

{ for (n=2, 10000, if (isprime(n), a=m=n; k=2, a=k*m; k++); write("b064924.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 29 2009

Formula

a(n) = A007917(n) * (A064722(n) + 1)