A283468 -id:A283468 - 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

A283471 Numbers n > 2 such that A004001(A004001(n-1)) = A004001(n-A004001(n-1)).

Original entry on oeis.org

3, 4, 6, 7, 8, 10, 13, 14, 15, 16, 18, 28, 29, 30, 31, 32, 34, 59, 60, 61, 62, 63, 64, 66, 122, 123, 124, 125, 126, 127, 128, 130, 249, 250, 251, 252, 253, 254, 255, 256, 258, 504, 505, 506, 507, 508, 509, 510, 511, 512, 514, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1026, 2038, 2039, 2040, 2041, 2042, 2043, 2044, 2045

Offset: 1

Antti Karttunen, Mar 18 2017

nonn

Equally, numbers n > 2 for which A004001(A004001(n-1)) = A004001(A080677(n-1)).

Antti Karttunen, Table of n, a(n) for n = 1..185

Positions of zeros in A283468 and A283470.
Cf. A004001, A080677, A283473.
Subsequence of A283482.

a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; Select[Range[3, 2^11], Function[n, a[#] == a[n - #] &@ a[n - 1]]] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)

A286541 Compound filter (the left & right summand of Hofstadter-Conway $10000 sequence): a(n) = P(A004001(A004001(n-1)), A004001(n-A004001(n-1))), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.

Original entry on oeis.org

0, 0, 1, 1, 2, 5, 5, 5, 8, 13, 19, 19, 25, 25, 25, 25, 32, 41, 51, 62, 62, 73, 86, 86, 99, 99, 99, 113, 113, 113, 113, 113, 128, 145, 163, 182, 202, 202, 222, 244, 267, 267, 290, 315, 315, 340, 340, 340, 366, 394, 394, 422, 422, 422, 451, 451, 451, 451, 481, 481, 481, 481, 481, 481, 512, 545, 579, 614, 650, 687, 687, 724, 763, 803, 844, 844, 885, 928, 972, 972

Offset: 1

Antti Karttunen, May 18 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Eric Weisstein's World of Mathematics, Pairing Function

Cf. A004001, A286559, A286560.

Cf. A283468, A283469, A283470, A283472 and also A283471, A283473.

(define (A286541 n) (if (<= n 2) 0 (* (/ 1 2) (+ (expt (+ (A004001 (A004001 (- n 1))) (A004001 (- n (A004001 (- n 1))))) 2) (- (A004001 (A004001 (- n 1)))) (- (* 3 (A004001 (- n (A004001 (- n 1)))))) 2))))

a(1) = a(2) = 0, for n > 2, a(n) = (1/2)*(2 + ((A004001(A004001(n-1))+A004001(n-A004001(n-1)))^2) - A004001(A004001(n-1)) - 3*A004001(n-A004001(n-1))).

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Scheme

Formula

Extensions

A283471 Numbers n > 2 such that A004001(A004001(n-1)) = A004001(n-A004001(n-1)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A286541 Compound filter (the left & right summand of Hofstadter-Conway $10000 sequence): a(n) = P(A004001(A004001(n-1)), A004001(n-A004001(n-1))), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.

Views

Author

Keywords

Links

Crossrefs

Programs

Scheme

Formula