A131854 -id:A131854 - cp's OEIS frontend

A131851 Real part of the function z(n)=Sum(d(k)i^k: d as in n=Sum(d(k)2^k), i=sqrt(-1)).

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

Offset: 0

Reinhard Zumkeller, Jul 22 2007

sign

A131852(n) = Im(z(n));
z(A000079(n))=(A056594(n),A056594(n+3)); a(A000079(n))=A056594(n);
a(A131854(n))=0; a(A131861(n))>0; a(A131859(n))=1; a(A131863(n))<0;
z(A131853(n))=(0,0); z(A131856(n))=(0,1); z(A131858(n))=(1,0); z(A131860(n))=(1,1);
for n>0: a(A131865(n))=n and ABS(a(m))A131865(n).

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

Cf. A007088.

z[0] = 0; z[n_] := z[n] = z[Floor[n/2]]*I + Mod[n, 2]; Table[z[n] // Re, {n, 0, 110}] (* Jean-François Alcover, Jul 03 2013 *)

z(n) = if n=0 then (0, 0) else z(floor(n/2))*(0, 1) + (n mod 2, 0), complex multiplication.

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 *)

A131855 Numbers m such that A131852(m) = 0.

Original entry on oeis.org

0, 1, 4, 5, 10, 11, 14, 15, 16, 17, 20, 21, 26, 27, 30, 31, 40, 41, 44, 45, 56, 57, 60, 61, 64, 65, 68, 69, 74, 75, 78, 79, 80, 81, 84, 85, 90, 91, 94, 95, 104, 105, 108, 109, 120, 121, 124, 125, 130, 131, 134, 135, 146, 147, 150, 151, 160, 161, 164, 165, 170, 171, 174

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

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

Cf. A131852, A131853, A131854, A131857, A131862, A131864.

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

A131856 Numbers m such that z(m)=(0,1) with z as defined in A131851.

Original entry on oeis.org

2, 7, 22, 32, 37, 42, 47, 52, 62, 67, 82, 87, 97, 107, 112, 117, 122, 127, 162, 167, 182, 227, 242, 247, 262, 292, 302, 322, 327, 342, 352, 357, 362, 367, 372, 382, 422, 482, 487, 502, 512, 517, 522, 527, 532, 542, 552, 557, 572, 577, 587, 592, 597, 602, 607

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

Intersection of A131854 and A131857: A131851(a(n))=0, A131852(a(n))=1.

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

Cf. A131851, A131853, A131858, A131860.

A131861 Numbers m such that A131851(m) > 0.

Original entry on oeis.org

1, 3, 9, 11, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 29, 31, 33, 35, 41, 43, 48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 61, 63, 81, 83, 89, 91, 113, 115, 121, 123, 129, 131, 137, 139, 144, 145, 146, 147, 149, 151, 152, 153, 154, 155, 157, 159, 161, 163, 169, 171, 176

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

Cf. A131862, A131854, A131859, A131863.

A131863 Numbers m such that A131851(m) < 0.

Original entry on oeis.org

4, 6, 12, 14, 36, 38, 44, 46, 64, 66, 68, 69, 70, 71, 72, 74, 76, 77, 78, 79, 84, 86, 92, 94, 96, 98, 100, 101, 102, 103, 104, 106, 108, 109, 110, 111, 116, 118, 124, 126, 132, 134, 140, 142, 164, 166, 172, 174, 192, 194, 196, 197, 198, 199, 200, 202, 204, 205, 206

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

Cf. A131864, A131854, A131859, A131861.

cp's OEIS Frontend

A131851 Real part of the function z(n)=Sum(d(k)*i^k: d as in n=Sum(d(k)*2^k), i=sqrt(-1)).

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

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A131855 Numbers m such that A131852(m) = 0.

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

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A131856 Numbers m such that z(m)=(0,1) with z as defined in A131851.

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A131861 Numbers m such that A131851(m) > 0.

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A131863 Numbers m such that A131851(m) < 0.

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A131851 Real part of the function z(n)=Sum(d(k)i^k: d as in n=Sum(d(k)2^k), i=sqrt(-1)).