A160855 a(n) is the smallest positive integer not occurring earlier in the sequence such that Sum_{k=1..n} a(k) written in binary contains binary n as a substring.
1, 3, 2, 6, 8, 4, 5, 11, 10, 24, 12, 13, 7, 9, 28, 17, 36, 14, 20, 46, 22, 44, 25, 18, 15, 16, 19, 21, 23, 26, 38, 33, 68, 30, 37, 29, 65, 39, 27, 57, 50, 88, 45, 85, 47, 83, 48, 34, 49, 51, 79, 53, 56, 32, 31, 35, 40, 41, 42, 63, 58, 72, 64, 66, 69, 61, 129, 93, 106, 60, 86
Offset: 1
Examples
From _Michael De Vlieger_, May 09 2017: (Start) a(1) = 1 since binary n = "1" appears in the binary total of all numbers in the sequence "1" at position 1. a(2) = 3 since binary n = "10" appears in the binary total of all numbers in the sequence (1 + 3) = "100" starting at position 1. a(3) = 2 since binary n = "11" appears in the binary total of all numbers in the sequence (1 + 3 + 2) = "110" starting at position 1. a(4) = 6 since binary n = "100" appears in the binary total of all numbers in the sequence (1 + 3 + 2 + 6) = "1100" starting at position 2. ... (End)
Links
- H. v. Eitzen, Table of n, a(n) for n=1..100000
- Rémy Sigrist, Colorized scatterplot of the first 100000 terms
- Rémy Sigrist, Alternate colorized scatterplot of the first 100000 terms
Programs
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Haskell
import Data.List (delete) a160855 n = a160855_list !! (n - 1) a160855_list = 1 : f 2 1 [2..] where f x sum zs = g zs where g (y:ys) = if binSub x (sum + y) then y : f (x + 1) (sum + y) (delete y zs) else g ys binSub u = sub where sub w = mod w m == u || w > u && sub (div w 2) m = a062383 u -- Reinhard Zumkeller, Jul 12 2015 -
Mathematica
a = {}; Do[k = 1; While[Or[MemberQ[a, k], SequencePosition[ IntegerDigits[Total@ a + k, 2], #] == {}], k++] &@ IntegerDigits[n, 2]; AppendTo[a, k], {n, 71}]; a (* Michael De Vlieger, May 09 2017, Version 10.1 *)
Formula
a(A236341(n)) = n. - Reinhard Zumkeller, Jul 12 2015
Extensions
Extended by Ray Chandler, Jun 15 2009
Comments