A131861 -id: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)).

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.

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

A131859 Numbers m such that A131851(m) = 1.

Original entry on oeis.org

1, 3, 9, 11, 16, 18, 21, 23, 24, 26, 29, 31, 33, 35, 41, 43, 48, 50, 53, 55, 56, 58, 61, 63, 81, 83, 89, 91, 113, 115, 121, 123, 129, 131, 137, 139, 144, 146, 149, 151, 152, 154, 157, 159, 161, 163, 169, 171, 176, 178, 181, 183, 184, 186, 189, 191, 209, 211, 217

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

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

Cf. A131851, A131858, A131857, A131859, A131861, A131863.

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.

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

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A131859 Numbers m such that A131851(m) = 1.

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

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

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

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A131859 Numbers m such that A131851(m) = 1.

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A131862 Numbers m such that A131852(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)).