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A263856 Let S_n be the list of the first n primes written in binary, with least significant bits on the left, and sorted into lexicographic order; a(n) = position of n-th prime in S_n. 4
1, 2, 2, 4, 4, 3, 2, 6, 9, 5, 11, 4, 3, 11, 14, 6, 13, 9, 11, 17, 3, 20, 14, 5, 2, 9, 23, 20, 12, 4, 31, 17, 5, 23, 12, 32, 17, 22, 32, 15, 26, 14, 42, 2, 11, 37, 29, 46, 27, 14, 9, 48, 6, 40, 2, 43, 22, 51, 18, 12, 43, 17, 39, 56, 14, 32, 45, 6, 50 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(A264647(n)) = n and a(m) != n for m < A264647(n). - Reinhard Zumkeller, Nov 19 2015

A264662(n,a(n)) = A000040(n): a(n) = index of prime(n) in n-th row of triangle A264662. - Reinhard Zumkeller, Nov 20 2015

LINKS

John Bodeen, Table of n, a(n) for n = 1..24771

OCaml program to generate the sequence

EXAMPLE

S_1 = [01], a(1) = 1;

S_2 = [01, 11], a(2) = 2;

S_3 = [01, 101, 11], a(3) = 2;

S_4 = [01, 101, 11, 111], a(4) = 4;

S_5 = [01, 101, 11, 1101, 111], a(5) = 4;

S_5 = [01, 101, 1011, 11, 1101, 111], a(6) = 3;

...

MAPLE

s:= proc(n) s(n):= cat("", convert(ithprime(n), base, 2)[]) end:

a:= n-> ListTools[BinarySearch](sort([seq(s(i), i=1..n)]), s(n)):

seq(a(n), n=1..100);  # Alois P. Heinz, Nov 19 2015

PROG

(Haskell)

import Data.List (insertBy); import Data.Function (on)

import Data.List (elemIndex); import Data.Maybe (fromJust)

a263856 n = a263856_list !! (n-1)

a263856_list = f [] a004676_list where

   f bps (x:xs) = y : f bps' xs where

     y = fromJust (elemIndex x bps') + 1

     bps' = insertBy (compare `on` (reverse . show)) x bps

-- Reinhard Zumkeller, Nov 19 2015

(Python)

from sympy import prime

def A263856(n):

    return 1+sorted(format(prime(i), 'b')[::-1] for i in range(1, n+1)).index(format(prime(n), 'b')[::-1]) # Chai Wah Wu, Nov 22 2015

CROSSREFS

A004676 is the sequence upon which the lexicographic ordering is based.

Cf. A264596.

Cf. A264647, A264662.

Sequence in context: A290633 A038674 A182923 * A090277 A024222 A196063

Adjacent sequences:  A263853 A263854 A263855 * A263857 A263858 A263859

KEYWORD

nonn,base

AUTHOR

John Bodeen, Oct 28 2015

STATUS

approved

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Last modified February 18 20:32 EST 2018. Contains 299330 sequences. (Running on oeis4.)