A338362 Inverse permutation to A283312.

1, 2, 4, 3, 6, 5, 8, 10, 11, 7, 12, 14, 15, 9, 17, 18, 19, 21, 22, 24, 25, 13, 26, 28, 29, 16, 30, 31, 32, 34, 35, 37, 38, 20, 39, 40, 41, 23, 43, 44, 45, 47, 48, 50, 51, 27, 52, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 33, 65, 67, 68, 36, 70, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82

Offset

1,2

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Formula

Let g(n) = A338363(n) = n + pi(n) - pi(n/2), where pi = A000720.

Then a(n) = g(n)-1 if n is a prime, a(n) = g(n/2) if n is twice a prime, and otherwise a(n) = g(n).

Maple

g := m -> m+pi(m)-pi(m/2); #  A338363
A338362 := proc(n) global g;
if isprime(n) then return(g(n)-1); fi;
if type(n, even) then
   if isprime(n/2) then return(g(n/2)); fi;
fi;
return(g(n)); end proc;
[seq(A338362(n), n=1..128)];

Mathematica

g[n_] := n + PrimePi[n] - PrimePi[n/2];
a[n_] := Which[PrimeQ[n], g[n]-1, PrimeQ[n/2], g[n/2], True, g[n]];
Table[a[n], {n, 1, 128}] (* Jean-François Alcover, Apr 04 2023 *)

Crossrefs

Cf. A000720, A283312, A338363.

Sequence in context: A338618 A114792 A113324 * A281117 A227114 A354373

Adjacent sequences: A338359 A338360 A338361 * A338363 A338364 A338365

Keyword

nonn

Author

N. J. A. Sloane, Nov 03 2020

Status

approved