A109400 For all k: the first k numbers followed by the first k primes.

1, 2, 1, 2, 2, 3, 1, 2, 3, 2, 3, 5, 1, 2, 3, 4, 2, 3, 5, 7, 1, 2, 3, 4, 5, 2, 3, 5, 7, 11, 1, 2, 3, 4, 5, 6, 2, 3, 5, 7, 11, 13, 1, 2, 3, 4, 5, 6, 7, 2, 3, 5, 7, 11, 13, 17, 1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 5, 7, 11, 13, 17, 19, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 5, 7, 11, 13, 17, 19, 23

Offset: 1

Author

Reinhard Zumkeller, Jun 27 2005

Keywords

• nonn

Comments

a(k*(k-1) + m) = a(A002378(k-1) + m) = m for 1<=m<=k;

a(k^2 + m) = a(A000290(k) + m) = A000040(m) for 1<=m<=k;

see A109401 for number of primes and A109402 for partial sums.

Examples

			1, 2; 1 2, 2 3; 1 2 3, 2 3 5; 1 2 3 4, 2 3 5 7; 1 2 ...
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002260, A037126, A082500, A000040.

Programs

Haskell

a109400 n = a109400_list !! (n-1)
a109400_list = concat $ zipWith (++) a002260_tabl a037126_tabl
-- Reinhard Zumkeller, Jun 23 2015, Dec 11 2011

Mathematica

With[{prs=Prime[Range[20]]},Flatten[Table[{Range[n],Take[prs,n]},{n,10}]]] (* Harvey P. Dale, Dec 08 2011 *)