A283470 -id:A283470 - cp's OEIS frontend

A283473 Numbers n for which A004001(n) = A283470(n).

1, 2, 5, 11, 12, 23, 24, 25, 26, 27, 50, 51, 52, 53, 54, 55, 56, 57, 58, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495

Offset: 1

Antti Karttunen, Mar 18 2017

nonn

Equally, numbers n such that A004001(n) = A283469(n).

Antti Karttunen, Table of n, a(n) for n = 1..803

Positions of zeros in A283472.

Cf. A004001, A283469, A283470, A283471.

a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; With[{nn = 500}, Function[s, Select[Range@ nn, a@ # == s[[#]] &]]@ Table[BitXor[a[#], a[n - #]] &@ a[n - 1] + Boole[n <= 2], {n, nn}]] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)

A283469 a(n) = A004001(A004001(n-1)) OR A004001(n-A004001(n-1)), a(1) = a(2) = 1.

Original entry on oeis.org

1, 1, 1, 1, 3, 2, 2, 2, 3, 3, 7, 7, 4, 4, 4, 4, 5, 5, 7, 7, 7, 7, 14, 14, 15, 15, 15, 8, 8, 8, 8, 8, 9, 9, 11, 11, 13, 13, 14, 15, 14, 14, 15, 15, 15, 15, 15, 15, 15, 29, 29, 30, 30, 30, 31, 31, 31, 31, 16, 16, 16, 16, 16, 16, 17, 17, 19, 19, 21, 21, 21, 23, 22, 23, 26, 26, 27, 27, 27, 27, 30, 31, 31, 31, 31, 31, 31, 30, 31, 31, 31, 31, 31

Offset: 1

Antti Karttunen, Mar 18 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A003986, A283470, A283472, A283473 (positions where coincides with A004001).

a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; Table[BitOr[a[#], a[n - #]] &@ a[n - 1], {n, 93}] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)

(define (A283469 n) (if (<= n 2) 1 (A003986bi (A004001 (A004001 (- n 1))) (A004001 (- n (A004001 (- n 1)))))))
;; A003986bi implements bitwise-OR (see A003986). Code for A004001 given under that entry.

a(1) = a(2) = 1; for n > 2, a(n) = A004001(A004001(n-1)) OR A004001(A080677(n-1)), where OR is bitwise-or (A003986)
Other identities. For all n >= 1:
a(n) = A283470(n) + A283472(n).
A004001(n) = a(n) + A283472(n).

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 *)

A283472 a(n) = A004001(A004001(n-1)) AND A004001(n-A004001(n-1)), a(1) = a(2) = 0.

Original entry on oeis.org

0, 0, 1, 1, 0, 2, 2, 2, 2, 3, 0, 0, 4, 4, 4, 4, 4, 5, 4, 5, 5, 6, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 9, 8, 9, 8, 8, 8, 8, 10, 10, 10, 11, 11, 12, 12, 12, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 16, 16, 16, 16, 16, 17, 16, 17, 16, 17, 17, 16, 18, 18, 16, 16, 16, 17, 18, 18, 16, 16, 16, 17, 17, 17, 18, 20, 20, 20, 21, 22, 22, 24, 24, 24, 24

Offset: 1

Antti Karttunen, Mar 18 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A004001, A004198, A283469, A283470, A283473 (positions of zeros).

a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; Table[BitAnd[a[#], a[n - #]] &@ a[n - 1] - Boole[n <= 2], {n, 97}] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)

(define (A283472 n) (if (<= n 2) 0 (A004198bi (A004001 (A004001 (- n 1))) (A004001 (- n (A004001 (- n 1)))))))
;; A004198bi implements bitwise-AND (see A004198). Code for A004001 given under that entry.

a(1) = a(2) = 0; for n > 2, a(n) = A004001(A004001(n-1)) AND A004001(A080677(n-1)), where AND is bitwise-and (A004198).
Other identities. For all n >= 1:
a(n) = A283469(n) - A283470(n).
A004001(n) = A283469(n) + a(n) = A283470(n) + 2*a(n).

A283468 a(n) = A004001(A004001(n-1)) - A004001(n-A004001(n-1)), a(1) = a(2) = 1.

Original entry on oeis.org

1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, -1, 0, 1, 2, 2, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, -1, 0, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 4, 3, 3, 3, 2, 3, 3, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 2, 3, 4, 4, 3, 4, 5, 6, 6, 5, 6, 7, 7, 6, 7, 7, 6, 6, 6, 5, 6, 7, 7, 6, 7, 7, 6, 6, 6, 5, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1

Offset: 1

Antti Karttunen, Mar 18 2017

sign

The only negative terms seem to be -1's, occurring as a(1+(2^n)), for n >= 2.

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A004001, A080677, A283471 (positions of zeros), A283469, A283470, A283472.

Cf. also A283655.

a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; Table[a[#] - a[n - #] &@ a[n - 1] + Boole[n <= 2], {n, 120}] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)

(define (A283468 n) (if (<= n 2) 1 (- (A004001 (A004001 (- n 1))) (A004001 (- n (A004001 (- n 1)))))))
;; Code for A004001 given under that entry.

a(1) = a(2) = 1; for n > 2, a(n) = A004001(A004001(n-1)) - A004001(A080677(n-1)).

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))).

A283677 a(n) = lcm(b(b(n)), b(n-b(n)+1)) where b(n) = A004001(n).

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 2, 6, 3, 12, 12, 4, 4, 4, 4, 20, 5, 30, 35, 35, 42, 24, 24, 56, 56, 56, 8, 8, 8, 8, 8, 72, 9, 90, 99, 36, 36, 60, 130, 70, 70, 154, 165, 165, 60, 60, 60, 195, 208, 208, 112, 112, 112, 240, 240, 240, 240, 16, 16, 16, 16, 16, 16, 272, 17, 306, 323, 340, 357, 357, 126, 198, 414, 72, 72, 456, 475, 494

Offset: 1

Altug Alkan, Mar 14 2017

See the order of certain subsequences in scatterplot link.

			a(4) = lcm(A004001(A004001(4)), A004001(4-A004001(4)+1)) = lcm(1, 2) = 2.

Altug Alkan, Table of n, a(n) for n = 1..10000
Altug Alkan, Alternative Scatterplot of A283677
Index entries for sequences related to lcm's

Cf. A004001, A080677.

Cf. also A283470, A283673.

b[1] = b[2] = 1; b[n_] := b[n] = b[b[n - 1]] + b[n - b[n - 1]]; Table[LCM[b[b[n]], b[n + 1 - b[n]]], {n, 1, 78}] (* Indranil Ghosh, Mar 14 2017 *)

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

(define (A283677 n) (lcm (A004001 (A004001 n)) (A004001 (+ 1 (- n (A004001 n)))))) ;; (Code for A004001 given under that entry). - Antti Karttunen, Mar 18 2017

a(n) = lcm(A004001(A004001(n)), A004001(A080677(n))). - Antti Karttunen, Mar 18 2017

cp's OEIS Frontend

A283473 Numbers n for which A004001(n) = A283470(n).

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A283469 a(n) = A004001(A004001(n-1)) OR A004001(n-A004001(n-1)), a(1) = a(2) = 1.

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

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A283472 a(n) = A004001(A004001(n-1)) AND A004001(n-A004001(n-1)), a(1) = a(2) = 0.

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A283468 a(n) = A004001(A004001(n-1)) - A004001(n-A004001(n-1)), a(1) = a(2) = 1.

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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.

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A283677 a(n) = lcm(b(b(n)), b(n-b(n)+1)) where b(n) = A004001(n).

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