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A284884
Positions of 1's in A284881.
4
1, 3, 7, 9, 13, 17, 19, 21, 25, 27, 31, 35, 37, 39, 43, 47, 49, 51, 55, 57, 61, 63, 67, 71, 73, 75, 79, 81, 85, 89, 91, 93, 97, 101, 103, 105, 109, 111, 115, 117, 121, 125, 127, 129, 133, 137, 139, 141, 145, 147, 151, 153, 157, 161, 163, 165, 169, 171, 175
OFFSET
1,2
COMMENTS
This sequence and A284882 and A284883 form a partition of the positive integers. Conjecture: for n>=1, we have a(n)-3n-3 in {0,1,2}, 3*n+1-A284883(n) in {0,1,2,3}, and 3*n-1-A284884(n) in {0,1,2}.
A284881 = (1,-1,1,0,-1,0,1,-1,1,0,-1,0,1,0,...); thus
A284882 = (2,5,8,11,15,18,...)
A284883 = (4,6,10,12,14,16,...)
A284884 = (1,3,7,9,13,17,...).
LINKS
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0, 1, 1, 0}}] &, {0}, 6] (* A284878 *)
d = Differences[s] (* A284881 *)
Flatten[Position[d, -1]] (* A284882 *)
d2 = Flatten[Position[d, 0]] (* A284883 *)
Flatten[Position[d, 1]] (* A284884 *)
d2/2 (* A284885 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 16 2017
STATUS
approved