A308495 a(n) is the position of the first occurrence of prime(n) in A027748.

2, 3, 5, 8, 13, 16, 22, 25, 32, 41, 45, 55, 62, 66, 73, 83, 94, 98, 109, 117, 120, 132, 138, 150, 166, 173, 177, 185, 188, 196, 224, 231, 243, 247, 267, 271, 284, 295, 303, 315, 327, 331, 353, 356, 364, 368, 394, 419, 426, 430, 439, 452, 456, 475, 487, 500

Offset: 1

Author

Peter Dolland, Jun 01 2019

Keywords

• nonn

Examples

			For n = 5: a(5) = 13, A027748(13) = A000040(5) = 11.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001221, A013939, A027748, A082186.

Programs

Haskell

-- expected to be part of A027748
a027748_list = concat (map a027748_row [1..])
minIdx [] _ = []
minIdx _ [] = []
minIdx (a:as) (b:bs)
    | a == b = 1 : (map succ (minIdx as bs))
    | otherwise = map succ (minIdx as (b:bs))
a308495_list = minIdx a027748_list a000040_list
a308495 n = a308495_list !! (n-1)

Maple

b:= proc(n) option remember; `if`(n=1, 1,
      b(n-1) +nops(ifactors(n)[2]))
    end:
a:= n-> b(ithprime(n)):
seq(a(n), n=1..60);  # Alois P. Heinz, Jun 06 2019

Mathematica

b[n_] := b[n] = If[n == 1, 1, b[n-1] + PrimeNu[n]];
a[n_] := b[Prime[n]];
Array[a, 60] (* Jean-François Alcover, Nov 27 2020, after Alois P. Heinz *)

PARI

a(n) = 1 + sum(k=1, prime(n), omega(k)); \\ Michel Marcus, Jun 05 2019

Formula

A027748(a(n)) = A000040(n).

a(n) = 1 + A013939(A000040(n)). - Charlie Neder, Jun 04 2019

a(n) = A082186(A000040(n)). - Alois P. Heinz, Jun 06 2019

a(n) = 1 + Sum_{k=1..n} floor(prime(n)/prime(k)). - Benoit Cloitre, Jan 11 2025