A131855 -id:A131855 - cp's OEIS frontend

A131852 Imaginary part of the function z defined in A131851.

0, 0, 1, 1, 0, 0, 1, 1, -1, -1, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, -1, -1, 0, 0, -1, -1, 0, 0, 1, 1, 2, 2, 1, 1, 2, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, -1, -1, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, -1, -1, 0, 0, -1, -1, 0, 0, 1, 1, 2, 2, 1, 1, 2, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 0

Offset: 0

Reinhard Zumkeller, Jul 22 2007

sign

a(A000079(n)) = A056594(n+3);
a(A131855(n)) = 0; a(A131862(n)) > 0; a(A131857(n)) = 1; a(A131864(n)) < 0;
for n > 0: a(A098704(n+1)) = n and abs(a(m)) < n for m < A098704(n+1).

R. Zumkeller, Table of n, a(n) for n = 0..10000

z[0] = 0; z[n_] := z[n] = z[Floor[n/2]]*I + Mod[n, 2]; Table[z[n] // Im, {n, 0, 120}] (* Jean-François Alcover, Mar 02 2019 *)

A131853 Numbers m such that z(m)=(0,0) with z as defined in A131851.

Original entry on oeis.org

0, 5, 10, 15, 20, 30, 40, 45, 60, 65, 75, 80, 85, 90, 95, 105, 120, 125, 130, 135, 150, 160, 165, 170, 175, 180, 190, 195, 210, 215, 225, 235, 240, 245, 250, 255, 260, 270, 300, 320, 325, 330, 335, 340, 350, 360, 365, 380, 390, 420, 430, 450, 455, 470, 480, 485

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

Intersection of A131854 and A131855: A131851(a(n))=0, A131852(a(n))=0;

conjecture: a(n) mod 5 = 0.

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Reinhard Zumkeller)

Cf. A131851, A131856, A131858, A131860, A008587.

z[n_] := z[n] = If[n == 0, 0, z[Floor[n/2]] I + Mod[n, 2]];
Flatten[Position[Table[z[n], {n, 0, 500}], 0] - 1] (* Jean-François Alcover, Oct 12 2021 *)

A131854 Numbers m such that A131851(m) = 0.

Original entry on oeis.org

0, 2, 5, 7, 8, 10, 13, 15, 20, 22, 28, 30, 32, 34, 37, 39, 40, 42, 45, 47, 52, 54, 60, 62, 65, 67, 73, 75, 80, 82, 85, 87, 88, 90, 93, 95, 97, 99, 105, 107, 112, 114, 117, 119, 120, 122, 125, 127, 128, 130, 133, 135, 136, 138, 141, 143, 148, 150, 156, 158, 160, 162, 165

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A131853, A131855, A131859, A131861, A131863.

Z:= proc(n) option remember;
I*procname(floor(n/2))+(n mod 2)
end proc:
Z(0):= 0:
select(Re@Z=0, [$0..1000]); # Robert Israel, Dec 18 2017

z[0] = 0; z[n_] := z[n] = z[Floor[n/2]]*I + Mod[n, 2]; Select[Range[0, 200], Re[z[#]] == 0&] (* Jean-François Alcover, Jan 31 2018 *)

isok(n) = {d = Vecrev(binary(n)); real(sum(k=1, #d, d[k]*I^(k-1))) == 0;} \\ Michel Marcus, Jan 31 2018

A131857 Numbers m such that A131852(m) = 1.

Original entry on oeis.org

2, 3, 6, 7, 18, 19, 22, 23, 32, 33, 36, 37, 42, 43, 46, 47, 48, 49, 52, 53, 58, 59, 62, 63, 66, 67, 70, 71, 82, 83, 86, 87, 96, 97, 100, 101, 106, 107, 110, 111, 112, 113, 116, 117, 122, 123, 126, 127, 162, 163, 166, 167, 178, 179, 182, 183, 226, 227, 230, 231, 242, 243

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A131856, A131854, A131855, A131862, A131864.

Z:= proc(n) option remember;
I*procname(floor(n/2))+(n mod 2)
end proc:
Z(0):= 0:
select(Im@Z=1, [$0..1000]); # Robert Israel, Dec 18 2017

z[0] = 0; z[n_] := z[n] = z[Floor[n/2]]*I + Mod[n, 2]; Select[Range[0, 250], Im[z[#]] == 1&] (* Jean-François Alcover, Jan 31 2018 *)

isok(n) = {d = Vecrev(binary(n)); imag(sum(k=1, #d, d[k]*I^(k-1))) == 1;} \\ Michel Marcus, Jan 31 2018

A131858 Numbers m such that z(m)=(1,0) with z as defined in A131851.

Original entry on oeis.org

1, 11, 16, 21, 26, 31, 41, 56, 61, 81, 91, 121, 131, 146, 151, 161, 171, 176, 181, 186, 191, 211, 241, 251, 256, 261, 266, 271, 276, 286, 296, 301, 316, 321, 331, 336, 341, 346, 351, 361, 376, 381, 386, 391, 406, 416, 421, 426, 431, 436, 446, 451, 466, 471

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

Intersection of A131855 and A131859: A131851(a(n))=1, A131852(a(n))=0.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A131851, A131853, A131856, A131860.

A131862 Numbers m such that A131852(m) > 0.

Original entry on oeis.org

2, 3, 6, 7, 18, 19, 22, 23, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 58, 59, 62, 63, 66, 67, 70, 71, 82, 83, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 106, 107, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 126, 127

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

Cf. A131861, A131855, A131857, A131864.

A131864 Numbers m such that A131852(m) < 0.

Original entry on oeis.org

8, 9, 12, 13, 24, 25, 28, 29, 72, 73, 76, 77, 88, 89, 92, 93, 128, 129, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 148, 149, 152, 153, 154, 155, 156, 157, 158, 159, 168, 169, 172, 173, 184, 185, 188, 189, 192, 193, 196, 197, 200, 201, 202, 203

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

Cf. A131863, A131855, A131857, A131862.

cp's OEIS Frontend

A131852 Imaginary part of the function z defined in A131851.

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A131853 Numbers m such that z(m)=(0,0) with z as defined in A131851.

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A131854 Numbers m such that A131851(m) = 0.

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A131857 Numbers m such that A131852(m) = 1.

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PARI

A131858 Numbers m such that z(m)=(1,0) with z as defined in A131851.

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A131862 Numbers m such that A131852(m) > 0.

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A131864 Numbers m such that A131852(m) < 0.

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