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

2,1

Comments

A064920(a(n)) = n.

Links

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

Formula

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

Example

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.

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A338702 A064919 A064923 * A196330 A332462 A358137

Adjacent sequences: A064921 A064922 A064923 * A064925 A064926 A064927

Keyword

nice,nonn,look

Author

Reinhard Zumkeller, Oct 14 2001

Status

approved