A082500 a(n) = ceiling(n/2) if n is odd, or prime(n/2) otherwise.

1, 2, 2, 3, 3, 5, 4, 7, 5, 11, 6, 13, 7, 17, 8, 19, 9, 23, 10, 29, 11, 31, 12, 37, 13, 41, 14, 43, 15, 47, 16, 53, 17, 59, 18, 61, 19, 67, 20, 71, 21, 73, 22, 79, 23, 83, 24, 89, 25, 97, 26, 101, 27, 103, 28, 107, 29, 109, 30, 113, 31, 127, 32, 131, 33, 137, 34, 139, 35, 149, 36

Offset: 1

Author

Reinhard Zumkeller, May 11 2003

Keywords

• nonn

Comments

Alternatively, list of pairs n, prime(n). - Zak Seidov, Feb 18 2005

a(n) = (n mod 2)*(n+1)/2 + (1 - n mod 2)*A000040(n/2);

k>0: a(2*k-1)=k, a(2*k)=A000040(k), A049084(a(2*k))=k; a(2*k-1)+a(2*k)=A014688(k).

Each prime occurs at two positions, the distances between them are: 1, 1, 3, 5, 11, 13, 19, 21, 27, 37, 39, 49, 55, 57, 63, 73, 83, 85, ... - Zak Seidov, Mar 06 2011

See A239636. - Reinhard Zumkeller, Mar 22 2014

Links

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

Crossrefs

A000027 and A000040 interleaved. - Omar E. Pol, Mar 13 2012

Programs

Haskell

import Data.List (transpose)
a082500 n = a082500_list !! (n-1)
a082500_list = concat $ transpose [[1..], a000040_list]
-- Reinhard Zumkeller, Mar 22 2014, Mar 19 2011, Oct 14 2010

Magma

[IsOdd(n) select Ceiling(n/2) else NthPrime(n div 2): n in[1..71]];  // Bruno Berselli, Mar 07 2011

Mathematica

s=Range[500];Do[s=Insert[s,Prime[n],2n],{n,100}];s (* Zak Seidov Mar 05 2011 *)
Table[If[OddQ[n],Ceiling[n/2 ],Prime[n/2]],{n,80}] (* Harvey P. Dale, Feb 22 2025 *)