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