A075158 Prime factorization of n+1 encoded with the run lengths of binary expansion.

0, 1, 2, 3, 5, 4, 10, 7, 6, 11, 21, 8, 42, 20, 9, 15, 85, 12, 170, 23, 22, 43, 341, 16, 13, 84, 14, 40, 682, 19, 1365, 31, 41, 171, 18, 24, 2730, 340, 86, 47, 5461, 44, 10922, 87, 17, 683, 21845, 32, 26, 27, 169, 168, 43690, 28, 45, 80, 342, 1364, 87381, 39, 174762

Offset

0,3

Comments

a(2n) = 1 or 2 mod 4 and a(2n+1) = 0 or 3 mod 4 for all n > 1

Links

Table of n, a(n) for n=0..60.

Index entries for sequences that are permutations of the natural numbers

Example

a(1) = 1 as 2 = 2^1, a(2) = 2 (10 in binary) as 3 = 3^1 * 2^0, a(3) = 3 (11) as 4 = 2^2, a(4) = 5 (101) as 5 = 5^1 * 3^0 * 2^0, a(5) = 4 (100) as 6 = 3^1 * 2^1, a(8) = 6 (110) as 9 = 3^2 * 2^0, a(11) = 8 (1000) as 12 = 3^1 * 2^2, a(89) = 35 (100011) as 90 = 5^1 * 3^2 * 2^1, a(90) = 90 (1011010) as 91 = 13^1 * 11^0 * 7^1 * 5^0 * 3^0 * 2^0.
The binary expansion of a(n) begins from the left with as many 1's as is the exponent of the largest prime present in the factorization of n+1 and from then on follows runs of ej+1 zeros and ones alternatively, where ej are the corresponding exponents of the successively lesser primes (0 if that prime does not divide n+1).

Prog

(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a075158 = fromJust . (`elemIndex` a075157_list)
-- Reinhard Zumkeller, Aug 04 2014

Crossrefs

Inverse of A075157. a(n) = A075160(n+1)-1. a(A006093(n)) = A000975(n). Cf. A059884.

Sequence in context: A374916 A100932 A064360 * A215526 A246841 A066417

Adjacent sequences: A075155 A075156 A075157 * A075159 A075160 A075161

Keyword

nonn

Author

Antti Karttunen, Sep 13 2002

Status

approved