The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A235726 Lexicographically earliest sequence of positive integers such that a(nm) != a(n + m) for all positive integers n and m such that nm != n + m. 1
 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 5, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) != a(n-1) because a(n*1) = a((n-1)+1). Records appear at: a(1) = 1, a(2) = 2, a(8) = 3, a(16) = 4, a(64) = 5, a(1024) = 6, a(4080) = 7, a(320000) = 8. From Robert Israel, Apr 19 2017: (Start) a(n) = 1 iff n is odd. If n == 2 (mod 4), then a(n) = 2. (End) LINKS Peter Kagey, Table of n, a(n) for n = 1..10000 EXAMPLE For n = 8, a(8) != 1 because a(1 + 7) != a(1 * 7); a(8) != 2 because a(2 * 4) != a(2 + 4); a(8) = 3. MAPLE N:= 100: # to get a(1) to a(N) A[1]:= 1: A[2]:= 2: A[3]:= 1: A[4]:= 2: for n from 5 to N do if n::odd then A[n]:= 1 else A[n]:= min({\$2..n} minus {seq(A[q+n/q], q=numtheory:-divisors(n) minus {1, n})}); fi od: seq(A[i], i=1..N); # Robert Israel, Apr 19 2017 PROG (Haskell) a 1 = 1 a 4 = 2 a n = head \$ filter (`notElem` disallowedValues) [1..] where disallowedValues = map a \$ (n-1) : filter ( n `mod` d == 0) [1..n] divisorSum d = d + n `div` d CROSSREFS Cf. A072670. Sequence in context: A356206 A318707 A363228 * A060938 A087942 A359237 Adjacent sequences: A235723 A235724 A235725 * A235727 A235728 A235729 KEYWORD nonn AUTHOR Peter Kagey, Apr 18 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 24 09:11 EDT 2023. Contains 365566 sequences. (Running on oeis4.)