A094290 a(n) = prime(A001511(n)), where A001511 is one more than the 2-adic valuation of n.

2, 3, 2, 5, 2, 3, 2, 7, 2, 3, 2, 5, 2, 3, 2, 11, 2, 3, 2, 5, 2, 3, 2, 7, 2, 3, 2, 5, 2, 3, 2, 13, 2, 3, 2, 5, 2, 3, 2, 7, 2, 3, 2, 5, 2, 3, 2, 11, 2, 3, 2, 5, 2, 3, 2, 7, 2, 3, 2, 5, 2, 3, 2, 17, 2, 3, 2, 5, 2, 3, 2, 7, 2, 3, 2, 5, 2, 3, 2, 11, 2, 3, 2, 5, 2, 3, 2, 7, 2, 3, 2, 5, 2, 3, 2, 13, 2, 3, 2, 5, 2, 3

Offset

1,1

Comments

Originally defined as: a(1) = 2 = prime(1). Then the first occurrence of prime(n) followed by all previous terms. i.e. If the index of first occurrence of prime(n) is k then the next k-1 terms are defined as a(k+r) = a(r), r = 1 to k-1. and a(2k) = prime(n+1) and so on.

Index of the first occurrence of prime(n)= 2^(n-1). Subsidiary sequences: If prime(n) is replaced by f(n) a large number of sequences can be obtained choosing f(n) = composite(n), f(n) = n^2,f(n) = n^r, r =3,4,5,..., f(n) = tau(n), f(n) = sigma(n), f(n) = n!, f(n) = Fibonacci(n), f(n) = T(n), triangular number, f(n) = n-th Bell, etc. each giving a distinct fascinating music.

The lexicographically earliest sequence such that no product of consecutive terms is a perfect square. - Joshua Zucker, Apr 30 2011

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A000040(A001511(n)). - Omar E. Pol, Sep 13 2013

Mathematica

Array[Prime[IntegerExponent[#, 2] + 1] &, 102] (* Michael De Vlieger, Nov 02 2018 *)

Prog

(PARI) A094290(n) = prime(1+valuation(n, 2)); \\ Antti Karttunen, Nov 02 2018
(Python)
from sympy import prime
def A094290(n): return prime((~n & n-1).bit_length()+1) # Chai Wah Wu, Jul 02 2022

Crossrefs

Cf. A000040, A001511.

Cf. also A115364.

Sequence in context: A066727 A076606 A056927 * A265111 A101876 A260218

Adjacent sequences: A094287 A094288 A094289 * A094291 A094292 A094293

Keyword

nonn

Author

Amarnath Murthy, Apr 28 2004

Extensions

Replaced the name with a formula given by Omar E. Pol, which is equivalent to the original definition. - Antti Karttunen, Nov 02 2018

Status

approved