A131859 -id:A131859 - 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

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.

A131860 Numbers m such that z(m)=(1,1) with z as defined in A131851.

Original entry on oeis.org

3, 18, 23, 33, 43, 48, 53, 58, 63, 83, 113, 123, 163, 178, 183, 243, 258, 263, 278, 288, 293, 298, 303, 308, 318, 323, 338, 343, 353, 363, 368, 373, 378, 383, 418, 423, 438, 483, 498, 503, 513, 523, 528, 533, 538, 543, 553, 568, 573, 593, 603, 633, 643, 658

Offset: 1

Reinhard Zumkeller, Jul 22 2007

nonn

Intersection of A131857 and A131859: A131851(a(n))=1, A131852(a(n))=1.

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

Cf. A131851, A131853, A131856, A131858.

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)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

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

Views

Author

Keywords

Comments

Links

Crossrefs

A131860 Numbers m such that z(m)=(1,1) with z as defined in A131851.

Views

Author

Keywords

Comments

Links

Crossrefs

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

Views

Author

Keywords

Crossrefs

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

Views

Author

Keywords

Crossrefs

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)).