A283677 -id:A283677 - cp's OEIS frontend

A283470 a(n) = A004001(A004001(n-1)) XOR A004001(n-A004001(n-1)), a(1) = a(2) = 1.

1, 1, 0, 0, 3, 0, 0, 0, 1, 0, 7, 7, 0, 0, 0, 0, 1, 0, 3, 2, 2, 1, 14, 14, 15, 15, 15, 0, 0, 0, 0, 0, 1, 0, 3, 2, 5, 5, 6, 7, 4, 4, 5, 4, 4, 3, 3, 3, 2, 29, 29, 30, 30, 30, 31, 31, 31, 31, 0, 0, 0, 0, 0, 0, 1, 0, 3, 2, 5, 4, 4, 7, 4, 5, 10, 10, 11, 10, 9, 9, 14, 15, 15, 14, 14, 14, 13, 10, 11, 11, 10, 9, 9, 6, 6, 6, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3

Offset: 1

Antti Karttunen, Mar 18 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..32768

Cf. A003987, A080677, A283468, A283469, A283472, A283471 (positions of zeros), A283473 (positions where coincides with A004001).

Cf. also A283677.

a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; Table[BitXor[a[#], a[n - #]] &@ a[n - 1] + Boole[n <= 2], {n, 107}] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)

(define (A283470 n) (if (<= n 2) 1 (A003987bi (A004001 (A004001 (- n 1))) (A004001 (- n (A004001 (- n 1)))))))
;; A003987bi implements bitwise-XOR (see A003987). Code for A004001 given under that entry.

a(n) = A004001(A004001(n-1)) XOR A004001(A080677(n-1)), where XOR is bitwise-xor (A003987)
Other identities. For all n >= 1:
a(n) = A283469(n) - A283472(n).
A004001(n) = a(n) + 2*A283472(n).

Erroneous b-file replaced by a correct one - Antti Karttunen, Feb 24 2018

A283673 a(n) = lcm(q(n - q(n+1) + 2), q(n - q(n) + 2)) where q(n) = A005185(n).

Original entry on oeis.org

1, 2, 2, 2, 6, 6, 3, 3, 3, 4, 15, 4, 5, 20, 5, 30, 30, 6, 6, 6, 6, 8, 24, 24, 8, 8, 8, 8, 10, 72, 72, 10, 110, 90, 99, 11, 110, 11, 132, 132, 12, 12, 12, 12, 12, 16, 70, 154, 112, 48, 84, 112, 112, 14, 16, 112, 16, 16, 16, 16, 20, 272, 238, 357, 304, 272, 380, 20, 340, 357, 399

Offset: 1

Altug Alkan, Mar 14 2017

See the order of chaotic subsequences in scatterplot link.

			a(4) = lcm(A005185(4 - A005185(5) + 2), A005185(4 - A005185(4) + 2)) = lcm(A005185(3), A005185(3)) = lcm(2, 2) = 2.

Altug Alkan, Table of n, a(n) for n = 1..10000
Altug Alkan, Alternative Scatterplot of A283673

Cf. A005185, A283672, A283677.

q[1] = q[2] = 1; q[n_] := q[n] = q[n - q[n - 1]] + q[n - q[n - 2]]; Table[LCM[q[n - q[n + 1] + 2], q[n - q[n] + 2]], {n, 71}] (* Indranil Ghosh, Mar 14 2017 *)

a=vector(1001); a[1]=a[2]=1; for(n=3, #a, a[n]=a[n-a[n-1]]+a[n-a[n-2]]); va = vector(1000, n, lcm(a[n+2-a[n+1]],a[n+2-a[n]]))

cp's OEIS Frontend

A283470 a(n) = A004001(A004001(n-1)) XOR A004001(n-A004001(n-1)), a(1) = a(2) = 1.

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