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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A281130 a(n+1) = a(n-a(n)) if a(n-1) < a(n), otherwise a(n+1) = 2*a(n); a(1) = a(2) = 1. 8
 1, 1, 2, 1, 2, 2, 4, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 8, 16, 16, 32, 4, 8, 16, 4, 8, 8, 16, 4, 8, 4, 8, 16, 16, 32, 16, 32, 8, 16, 8, 16, 4, 8, 32, 4, 8, 8, 16, 8, 16, 16, 32, 16, 32, 4, 8, 16, 16, 32, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The sequence is well defined, namely a(n) < n (with the exception of a(1)). Proof: Suppose a(s) = s+m, with m >= 0, is the first occurrence of a(n) >= n. It follows that a(s-1) = a(s-2) = (s+m)/2 and from there it follows that a(s-2-(s+m)/2) = (s+m)/2, but s-2-(s+m)/2 < (s+m)/2 which is a contradiction to the first statement. - Rok Cestnik, Aug 29 2017 From Robert G. Wilson v, Jan 16 2017: (Start) a(n) = 2^k, k >= 0. a(n)=1 for n: 1, 2, 4; a(n)=2 for n: 3, 5, 6, 8, 10, 14; a(n)=4 for n: 7, 9, 11, 12, 15, 16, 18, 20, 24, 28, 32, 42, 45, 49, 51, 62, 65, 75, 82, 84, 101, 108, 110, 118, 127, 175, 240; First occurrence of 2^k (A281131): 1, 3, 7, 13, 23, 41, 98, 223, 437, 699, 1213, 2624, 4674, 11163, 21300, 40858, 73977, etc.; Last occurrence of 2^k: 4, 14, 240, 1314, 10565, 35893, 62417, 638149, 2030926, etc.; Number of occurrences of 2^k: 3, 6, 27, 77, 167, 330, 706, 1756, 3811, etc. (End) LINKS Rok Cestnik, Table of n, a(n) for n = 1..10000 Rok Cestnik, Self-referencing visualization EXAMPLE a(3) = 2*a(2) = 2 because a(1) !< a(2). a(4) = a(3-a(3)) = 1 because a(2) < a(3). MATHEMATICA a[n_] := a[n] = If[a[n -2] < a[n -1], a[n -1 -a[n -1]], 2 a[n -1]]; a[1] = a[2] = 1; Array[a, 100] PROG (C) #include #include int main(void){ int N = 1000; int *a = (int*)malloc((N+1)*sizeof(int)); printf("1 1\n2 1\n"); a[1] = 1; a[2] = 1; for(int i = 2; i < N; ++i){ if(a[i-1] < a[i]) a[i+1] = a[i-a[i]]; else a[i+1] = 2*a[i]; printf("%d %d\n", i+1, a[i+1]); } return 0; } CROSSREFS Cf. A281131, A291598. Sequence in context: A139318 A205779 A205551 * A054541 A277891 A102722 Adjacent sequences: A281127 A281128 A281129 * A281131 A281132 A281133 KEYWORD nonn AUTHOR Rok Cestnik, Jan 15 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 23 04:30 EDT 2023. Contains 365532 sequences. (Running on oeis4.)