

A094290


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


3



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
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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 k1 terms are defined as a(k+r) = a(r), r = 1 to k1. and a(2k) = prime(n+1) and so on.
Index of the first occurrence of prime(n)= 2^(n1). 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) = nth 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 & n1).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



