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 A075158 Prime factorization of n+1 encoded with the run lengths of binary expansion. 17
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A247225 A100932 A064360 * A215526 A246841 A066417 Adjacent sequences:  A075155 A075156 A075157 * A075159 A075160 A075161 KEYWORD nonn AUTHOR Antti Karttunen, Sep 13 2002 STATUS approved

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Last modified May 25 06:16 EDT 2020. Contains 334581 sequences. (Running on oeis4.)