login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112049 a(n) = position of A112046(n) in A000040. 17
1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 4, 3, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 4, 5, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 6, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 4, 3, 1, 1, 2, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A112051 gives the first positions of distinct new values in this sequence, that seem also to be the positions of the first occurrence of each n, and thus the positions of the records. Compare also to A084921. - Antti Karttunen, May 26 2017

LINKS

Indranil Ghosh (terms 1..1000) & Antti Karttunen, Table of n, a(n) for n = 1..32768

FORMULA

a(n) = A049084(A112046(n)).

MATHEMATICA

a112046[n_]:=Block[{i=1}, While[JacobiSymbol[i, 2n + 1]==1, i++]; i]; a049084[n_]:=If[PrimeQ[n], PrimePi[n], 0]; Table[a049084[a112046[n]], {n, 102}] (* Indranil Ghosh, May 11 2017 *)

PROG

(PARI) A112049(n) = for(i=1, (2*n), if((kronecker(i, (n+n+1)) < 1), return(primepi(i)))); \\ Antti Karttunen, May 26 2017

(Python)

from sympy import jacobi_symbol as J, isprime, primepi

def a049084(n):

    return primepi(n) if isprime(n) else 0

def a112046(n):

    i=1

    while True:

        if J(i, 2*n + 1)!=1: return i

        else: i+=1

def a(n): return a049084(a112046(n))

print([a(n) for n in range(1, 103)]) # Indranil Ghosh, May 11 2017

CROSSREFS

Cf. A049084, A112046, A112051, A112060, A165471, A268829, A286465, A286466.

Cf. A286579 (ordinal transform).

Sequence in context: A293681 A293773 A071017 * A055230 A290262 A112050

Adjacent sequences:  A112046 A112047 A112048 * A112050 A112051 A112052

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 27 2005

EXTENSIONS

Unnecessary fallback-clause removed from the name by Antti Karttunen, May 26 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)