A284013 -id:A284013 - cp's OEIS frontend

A317841 Möbius transform of A284013 (= n - A002487(n)), where A002487 is Stern's Diatomic sequence.

0, 1, 1, 2, 2, 2, 4, 4, 4, 4, 6, 4, 8, 6, 8, 8, 12, 6, 12, 8, 8, 10, 16, 8, 16, 12, 14, 12, 22, 8, 26, 16, 20, 16, 20, 12, 26, 18, 20, 16, 30, 12, 30, 20, 18, 22, 38, 16, 36, 20, 26, 24, 40, 18, 36, 24, 34, 28, 48, 16, 52, 30, 40, 32, 48, 20, 56, 32, 38, 24, 58, 24, 58, 36, 30, 36, 50, 24, 66, 32, 48, 40, 64, 24, 50, 42

Offset: 1

Antti Karttunen, Aug 09 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to Stern's sequences

Cf. A002487, A008683, A284013, A317839.

A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
A284013(n) = (n - A002487(n));
A317841(n) = sumdiv(n,d,moebius(n/d)*A284013(d));

a(n) = Sum_{d|n} A008683(n/d)*A284013(d).

a(n) = A000010(n) - A317839(n).

A317842 Dirichlet convolution of A284013 (= n - A002487(n)) with itself, where A002487 is Stern's Diatomic sequence.

Original entry on oeis.org

0, 0, 0, 1, 0, 2, 0, 6, 1, 4, 0, 14, 0, 8, 4, 23, 0, 18, 0, 26, 8, 12, 0, 58, 4, 16, 10, 46, 0, 52, 0, 72, 12, 24, 16, 94, 0, 24, 16, 104, 0, 80, 0, 70, 42, 32, 0, 190, 16, 64, 24, 90, 0, 106, 24, 172, 24, 44, 0, 248, 0, 52, 66, 201, 32, 136, 0, 130, 32, 152, 0, 342, 0, 52, 80, 134, 48, 164, 0, 334, 63, 60, 0, 364, 48, 60, 44

Offset: 1

Antti Karttunen, Aug 09 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to Stern's sequences

Cf. A002487, A284013, A317839, A317841, A317843.

A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
A284013(n) = (n - A002487(n));
A317842(n) = sumdiv(n,d,A284013(n/d)*A284013(d));

a(n) = Sum_{d|n} A284013(n/d)*A284013(d).

A284007 a(n) = a(a(n-A002487(n))) + a(n-a(n-A002487(n))) with a(1) = a(2) = 1, where A002487 = Stern-Brocot sequence.

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 7, 8, 8, 9, 10, 11, 11, 11, 12, 12, 14, 13, 14, 14, 15, 16, 15, 16, 16, 18, 18, 18, 19, 19, 20, 20, 22, 22, 24, 23, 25, 24, 25, 25, 25, 26, 26, 27, 27, 28, 29, 28, 30, 29, 30, 31, 30, 32, 34, 34, 33, 33, 34, 34, 36, 37, 36, 37, 38, 38, 40, 41, 39, 40, 43, 42, 44, 43, 43, 44, 44, 45, 45, 45, 50

Offset: 1

Antti Karttunen, Mar 23 2017

nonn

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

Cf. A002487, A004001, A283474, A284000, A284007, A284013.

a(1) = a(2) = 1, for n > 2, a(n) = a(a(A284013(n))) + a(n-a(A284013(n))).

A283474 a(0) = 0, a(1) = 1, for n > 1, a(n) = a(n-1) + a(n-A002487(n)).

Original entry on oeis.org

0, 1, 2, 3, 6, 8, 14, 20, 40, 48, 68, 82, 150, 190, 272, 354, 708, 858, 1130, 1280, 2138, 2328, 3186, 3894, 7080, 8210, 10538, 11818, 20028, 23214, 33752, 44290, 88580, 100398, 123612, 134150, 222730, 233268, 277558, 300772, 534040, 567792, 691404, 725156, 1025928, 1126326, 1427098, 1704656, 3131754, 3665794

Offset: 0

Antti Karttunen, Mar 23 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..1024

Cf. A000045, A002487, A078510, A284007, A284013.

Cf. A283479 (first differences).

a(0) = 0, a(1) = 1, for n > 1, a(n) = a(n-1) + a(A284013(n)).

A283979 a(n) = (n XOR A264977(n))/4, where XOR is bitwise-xor (A003987).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 2, 3, 0, 3, 0, 0, 0, 7, 6, 5, 4, 4, 6, 7, 0, 5, 6, 5, 0, 7, 0, 0, 0, 15, 14, 9, 12, 10, 10, 9, 8, 10, 8, 8, 12, 10, 14, 15, 0, 9, 10, 15, 12, 14, 10, 9, 0, 9, 14, 9, 0, 15, 0, 0, 0, 31, 30, 17, 28, 22, 18, 21, 24, 20, 20, 18, 20, 16, 18, 17, 16, 22, 20, 22, 16, 21, 16, 16, 24, 16, 20, 18, 28, 22, 30, 31, 0, 17, 18, 27, 20, 28, 30

Offset: 0

Antti Karttunen, Mar 25 2017

Antti Karttunen, Table of n, a(n) for n = 0..8191
Index entries for sequences related to binary expansion of n

Cf. A003987, A264977, A265397, A284013.

A264977[n_]:= If[n<2, n, If[EvenQ[n], 2 A264977[n/2], BitXor[A264977[(n - 1)/2], A264977[(n + 1)/2]]]]; Table[BitXor[n, A264977[n]]/4, {n, 0, 100}] (* Indranil Ghosh, Mar 28 2017 *)

a(n) = if(n<2, n, if(n%2, bitxor(a((n - 1)/2), a((n + 1)/2)), 2*a(n/2)));
for(n=0, 150, print1(bitxor(n, a(n))/4,", ")) \\ Indranil Ghosh, Mar 28 2017

(define (A283979 n) (/ (A003987bi n (A264977 n)) 4)) ;; Where A003987bi implements bitwise-xor (A003987).

a(n) = (n XOR A264977(n))/4, where XOR is bitwise-xor (A003987).

cp's OEIS Frontend

A317841 Möbius transform of A284013 (= n - A002487(n)), where A002487 is Stern's Diatomic sequence.

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A317842 Dirichlet convolution of A284013 (= n - A002487(n)) with itself, where A002487 is Stern's Diatomic sequence.

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A284007 a(n) = a(a(n-A002487(n))) + a(n-a(n-A002487(n))) with a(1) = a(2) = 1, where A002487 = Stern-Brocot sequence.

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A283474 a(0) = 0, a(1) = 1, for n > 1, a(n) = a(n-1) + a(n-A002487(n)).

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A283979 a(n) = (n XOR A264977(n))/4, where XOR is bitwise-xor (A003987).

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