A102370 -id:A102370 - cp's OEIS frontend

A000035 Period 2: repeat [0, 1]; a(n) = n mod 2; parity of n.

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0

Offset: 0

N. J. A. Sloane

Least significant bit of n, lsb(n).
Also decimal expansion of 1/99.
Also the binary expansion of 1/3. - Robert G. Wilson v, Sep 01 2015
a(n) = A134451(n) mod 2. - Reinhard Zumkeller, Oct 27 2007 [Corrected by Jianing Song, Nov 22 2019]
Characteristic function of odd numbers: a(A005408(n)) = 1, a(A005843(n)) = 0. - Reinhard Zumkeller, Sep 29 2008
A102370(n) modulo 2. - Philippe Deléham, Apr 04 2009
Base b expansion of 1/(b^2-1) for any b >= 2 is 0.0101... (A005563 has b^2-1). - Rick L. Shepherd, Sep 27 2009
Let A be the Hessenberg n X n matrix defined by: A[1,j] = j mod 2, A[i,i] := 1, A[i,i-1] = -1, and A[i,j] = 0 otherwise. Then, for n >= 1, a(n) = (-1)^n*charpoly(A,1). - Milan Janjic, Jan 24 2010
From R. J. Mathar, Jul 15 2010: (Start)
The sequence is the principal Dirichlet character of the reduced residue system mod 2 or mod 4 or mod 8 or mod 16 ...
Associated Dirichlet L-functions are for example L(2,chi) = Sum_{n>=1} a(n)/n^2 == A111003,
or L(3,chi) = Sum_{n>=1} a(n)/n^3 = 1.05179979... = 7*A002117/8,
or L(4,chi) = Sum_{n>=1} a(n)/n^4 = 1.014678... = A092425/96. (End)
Also parity of the nonnegative integers A001477. - Omar E. Pol, Jan 17 2012
a(n) = (4/n), where (k/n) is the Kronecker symbol. See the Eric Weisstein link. - Wolfdieter Lang, May 28 2013
Also the inverse binomial transform of A131577. - Paul Curtz, Nov 16 2016 [an observation forwarded by Jean-François Alcover]
The emanation sequence for the globe category. That is take the globe category, take the corresponding polynomial comonad, consider its carrier polynomial as a generating function, and take the corresponding sequence. - David Spivak, Sep 25 2020
For n > 0, a(n) is the alternating sum of the product of n increasing and n decreasing odd factors. For example, a(4) = 1*7 - 3*5 + 5*3 - 7*1 and a(5) = 1*9 - 3*7 + 5*5 - 7*3 + 9*1. - Charlie Marion, Mar 24 2022

			G.f. = x + x^3 + x^5 + x^7 + x^9 + x^11 + x^13 + x^15 + ... - _Michael Somos_, Feb 20 2024

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

David Wasserman, Table of n, a(n) for n = 0..1000
Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
F. Javier de Vega, An extension of Furstenberg's theorem of the infinitude of primes, arXiv:2003.13378 [math.NT], 2020.
Clark Kimberling, A Combinatorial Classification of Triangle Centers on the Line at Infinity, J. Int. Seq., Vol. 22 (2019), Article 19.5.4.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Eric Weisstein's World of Mathematics, Dirichlet Series Generating Function
Eric Weisstein's World of Mathematics, Kronecker Symbol
A. K. Whitford, Binet's Formula Generalized, Fibonacci Quarterly, Vol. 15, No. 1, 1979, pp. 21, 24, 29
Index entries for "core" sequences
Index entries for sequences that are fixed points of mappings
Index entries for characteristic functions
Index entries for linear recurrences with constant coefficients, signature (0,1).

Ones complement of A059841.
Cf. A053644 for most significant bit.
This is Guy Steele's sequence GS(1, 2) (see A135416).
Period k zigzag sequences: this sequence (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), A271751 (k=10), A271832 (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18).
Cf. A154955 (Mobius transform), A131577 (binomial transform).
Cf. A111003 (Dgf at s=2), A233091 (Dgf at s=3), A300707 (Dgf at s=4).
Parity of A005811.

a000035 n = n `mod` 2  -- James Spahlinger, Oct 08 2012

a000035_list = cycle [0,1]  -- Reinhard Zumkeller, Jan 06 2012

A000035 := n->n mod 2;
[ seq(i mod 2, i=0..100) ];

PadLeft[{},110,{0,1}] (* Harvey P. Dale, Sep 25 2011 *)

A000035(n):=mod(n,2)$
makelist(A000035(n),n,0,30); /* Martin Ettl, Nov 12 2012 */

PARI
```
a(n)=n%2;
```

a(n)=direuler(p=1,100,if(p==2,1,1/(1-X)))[n] /* Ralf Stephan, Mar 27 2015 */

def A000035(n): return n & 1 # Chai Wah Wu, May 25 2022

(define (A000035 n) (mod n 2)) ;; For R6RS. Use modulo in older Schemes like MIT/GNU Scheme. - Antti Karttunen, Mar 21 2017

a(n) = (1 - (-1)^n)/2.
a(n) = n mod 2.
a(n) = 1 - a(n-1).
Multiplicative with a(p^e) = p mod 2. - David W. Wilson, Aug 01 2001
G.f.: x/(1-x^2). E.g.f.: sinh(x). - Paul Barry, Mar 11 2003
a(n) = (A000051(n) - A014551(n))/2. - Mario Catalani (mario.catalani(AT)unito.it), Aug 30 2003
a(n) = ceiling((-2)^(-n-1)). - Reinhard Zumkeller, Apr 19 2005
Dirichlet g.f.: (1-1/2^s)*zeta(s). - R. J. Mathar, Mar 04 2011
a(n) = ceiling(n/2) - floor(n/2). - Arkadiusz Wesolowski, Sep 16 2012
a(n) = ceiling( cos(Pi*(n-1))/2 ). - Wesley Ivan Hurt, Jun 16 2013
a(n) = floor((n-1)/2) - floor((n-2)/2). - Mikael Aaltonen, Feb 26 2015
Dirichlet g.f.: L(chi(2),s) with chi(2) the principal Dirichlet character modulo 2. - Ralf Stephan, Mar 27 2015
a(n) = 0^^n = 0^(0^(0...)) (n times), where we take 0^0 to be 1. - Natan Arie Consigli, May 02 2015
Euler transform and inverse Moebius transform of length 2 sequence [0, 1]. - Michael Somos, Feb 20 2024

A077957 Powers of 2 alternating with zeros.

Original entry on oeis.org

1, 0, 2, 0, 4, 0, 8, 0, 16, 0, 32, 0, 64, 0, 128, 0, 256, 0, 512, 0, 1024, 0, 2048, 0, 4096, 0, 8192, 0, 16384, 0, 32768, 0, 65536, 0, 131072, 0, 262144, 0, 524288, 0, 1048576, 0, 2097152, 0, 4194304, 0, 8388608, 0, 16777216, 0, 33554432, 0, 67108864, 0, 134217728, 0, 268435456

Offset: 0

N. J. A. Sloane, Nov 17 2002

Normally sequences like this are not included, since with the alternating 0's deleted it is already in the database.
Inverse binomial transform of A001333. - Paul Barry, Feb 25 2003
"Sloping binary representation" of powers of 2 (A000079), slope=-1 (see A037095 and A102370). - Philippe Deléham, Jan 04 2008
0,1,0,2,0,4,0,8,0,16,... is the inverse binomial transform of A000129 (Pell numbers). - Philippe Deléham, Oct 28 2008
Number of maximal self-avoiding walks from the NW to SW corners of a 3 X n grid.
Row sums of the triangle in A204293. - Reinhard Zumkeller, Jan 14 2012
Pisano period lengths: 1, 1, 4, 1, 8, 4, 6, 1, 12, 8, 20, 4, 24, 6, 8, 1, 16, 12, 36, 8, ... . - R. J. Mathar, Aug 10 2012
This sequence occurs in the length L(n) = sqrt(2)^n of Lévy's C-curve at the n-th iteration step. Therefore, L(n) is the Q(sqrt(2)) integer a(n) + a(n-1)*sqrt(2), with a(-1) = 0. For a variant of this C-curve see A251732 and A251733. - Wolfdieter Lang, Dec 08 2014
a(n) counts walks (closed) on the graph G(1-vertex,2-loop,2-loop). Equivalently the middle entry (2,2) of A^n where the adjacency matrix of digraph is A=(0,1,0;1,0,1;0,1,0). - David Neil McGrath, Dec 19 2014
a(n-2) is the number of compositions of n into even parts. For example, there are 4 compositions of 6 into even parts: (6), (222), (42), and (24). - David Neil McGrath, Dec 19 2014
Also the number of alternately constant compositions of n + 2, ranked by A351010. The alternately strict version gives A000213. The unordered version is A035363, ranked by A000290, strict A035457. - Gus Wiseman, Feb 19 2022
a(n) counts degree n fixed points of GF(2)[x]'s automorphisms. Proof: given a field k, k[x]'s automorphisms are determined by k's automorphisms and invertible affine maps x -> ax + b. GF(2) is rigid and has only one unit so its only nontrivial automorphism is x -> x + 1. For n = 0 we have 1 fixed point, the constant polynomial 1. (Taking the convention that 0 is not a degree 0 polynomial.) For n = 1 we have 0 fixed points as x -> x + 1 -> x are the only degree 1 polynomials. Note that if f(x) is a fixed point, then f(x) + 1 is also a fixed point. Given f(x) a degree n fixed point, we can assume WLOG x | f(x). Applying the automorphism, we then have x + 1 | f(x). Now note that f(x) / (x^2 + x) must be a fixed point, so any fixed point of degree n must either be of the form g(x) * (x^2 + x) or g(x) * (x^2 + x) + 1 for a unique degree n - 2 fixed point g(x). Therefore we have the recurrence relation a(n) = 2 * a(n - 2) as desired. - Keith J. Bauer, Mar 19 2024

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,2).

Cf. A000079, A077966.
Column k=3 of A219946. - Alois P. Heinz, Dec 01 2012
Cf. A016116 (powers repeated).

Flat(List([0..30],n->[2^n,0])); # Muniru A Asiru, Aug 05 2018

a077957 = sum . a204293_row  -- Reinhard Zumkeller, Jan 14 2012

&cat [[2^n,0]: n in [0..20]]; // Vincenzo Librandi, Apr 03 2018

seq(op([2^n,0]),n=0..100); # Robert Israel, Dec 23 2014

a077957[n_] := Riffle[Table[2^i, {i, 0, n - 1}], Table[0, {n}]]; a077957[29] (* Michael De Vlieger, Dec 22 2014 *)
CoefficientList[Series[1/(1 - 2*x^2), {x,0,50}], x] (* G. C. Greubel, Apr 12 2017 *)
LinearRecurrence[{0, 2}, {1, 0}, 54] (* Robert G. Wilson v, Jul 23 2018 *)
Riffle[2^Range[0,30],0,{2,-1,2}] (* Harvey P. Dale, Jan 06 2022 *)

PARI
```
a(n)=if(n<0||n%2, 0, 2^(n/2))
```

def A077957():
    x, y = -1, 1
    while True:
        yield -x
        x, y = x + y, x - y
a = A077957(); [next(a) for i in range(40)]  # Peter Luschny, Jul 11 2013

G.f.: 1/(1-2*x^2).
E.g.f.: cosh(x*sqrt(2)).
a(n) = (1 - n mod 2) * 2^floor(n/2).
a(n) = sqrt(2)^n*(1+(-1)^n)/2. - Paul Barry, May 13 2003
a(n) = 2*a(n-2) with a(0)=1, a(1)=0. - Jim Singh, Jul 12 2018

A062289 Numbers n such that n-th row in Pascal triangle contains an even number, i.e., A048967(n) > 0.

Original entry on oeis.org

2, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset: 1

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 02 2001

nonn

Numbers n such that binary representation contains the bit string "10". Union of A043569 and A101082. - Rick L. Shepherd, Nov 29 2004

The asymptotic density of this sequence is 1 (Burns, 2016). - Amiram Eldar, Jan 26 2021

Reinhard Zumkeller, Table of n, a(n) for n = 1..10001
Rob Burns, Asymptotic density of Catalan numbers modulo 3 and powers of 2, arXiv:1611.03705 [math.NT], 2016.
Oliver Kullmann and Xishun Zhao, On variables with few occurrences in conjunctive normal forms, in: K. A. Sakallah and L. Simon (eds), International Conference on Theory and Applications of Satisfiability Testing, Springer, Berlin, Heidelberg, 2011, pp. 33-46; arXiv preprint, arXiv:1010.5756 [cs.DM], 2010-2011.
Oliver Kullmann and Xishun Zhao, Parameters for minimal unsatisfiability: Smarandache primitive numbers and full clauses, arXiv preprint, arXiv:1505.02318 [cs.DM], 2015.

Complement of A000225, so these might be called non-Mersenne numbers.
A132782 is a subsequence.
Cf. A048967, A057716, A043569, A101082.
Cf. A007461, A036987, A102370, A105027.
Cf. A261461, A261922.

a062289 n = a062289_list !! (n-1)
a062289_list = 2 : g 2 where
   g n = nM n : g (n+1)
   nM k = maximum $ map (\i -> i + min i (a062289 $ k-i+1)) [2..k]
   -- Cf. link [Oliver Kullmann, Xishun Zhao], Def. 3.1, page 3.
-- Reinhard Zumkeller, Feb 21 2012, Dec 31 2010

ok[n_] := MatchQ[ IntegerDigits[n, 2], {_, 1, 0, _}]; Select[ Range[100], ok] (* Jean-François Alcover, Dec 12 2011, after Rick L. Shepherd *)

isok(m) = #select(x->((x%2)==0), vector(m+1, k, binomial(m, k-1))); \\ Michel Marcus, Jan 26 2021

def A062289(n): return n+(m:=n.bit_length())-(not n>=(1<Chai Wah Wu, Jun 30 2024

a(n) = A057716(n+1) - 1.
a(n) = 2 if n=1, otherwise max{min{2*i, a(n-i+1) + i}: 1 < i <= n}.
A036987(a(n)) = 0. - Reinhard Zumkeller, Mar 06 2012
A007461(a(n)) mod 2 = 0. - Reinhard Zumkeller, Apr 02 2012
A102370(n) = A105027(a(n)). - Reinhard Zumkeller, Jul 21 2012
A261461(a(n)) = A261922(a(n)). - Reinhard Zumkeller, Sep 17 2015

More terms from Rick L. Shepherd, Nov 29 2004

A105027 Write numbers in binary under each other; to get the next block of 2^k (k >= 0) terms of the sequence, start at 2^k, read diagonals in upward direction and convert to decimal.

Original entry on oeis.org

0, 1, 3, 2, 6, 5, 4, 7, 15, 10, 9, 8, 11, 14, 13, 12, 28, 23, 18, 17, 16, 19, 22, 21, 20, 31, 26, 25, 24, 27, 30, 29, 61, 44, 39, 34, 33, 32, 35, 38, 37, 36, 47, 42, 41, 40, 43, 46, 45, 60, 55, 50, 49, 48, 51, 54, 53, 52, 63, 58, 57, 56, 59, 62, 126, 93, 76, 71, 66, 65, 64, 67, 70

Offset: 0

N. J. A. Sloane, Apr 03 2005

This is a permutation of the nonnegative integers.
Structure: blocks of size 2^k - 1 taken from A102370, interspersed with terms of A102371. - Philippe Deléham, Nov 17 2007
a(A062289(n)) = A102370(n) for n > 0; a(A000225(n)) = A102371(n); a(A214433(n)) = A105025(a(n)). - Reinhard Zumkeller, Jul 21 2012

			        0
        1
       10
       11
   -> 100  Starting here, the upward diagonals
      101  read 110, 101, 100, 111, giving the block 6, 5, 4, 7.
      110
      111
     1000
     1001
     1010
     1011
      ...

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
Index entries for sequences that are permutations of the natural numbers
Index entries for sequences related to binary expansion of n

Cf. A102370, A105025, A105026, A105028.
Cf. A070939, A000079.
Cf. A214414 (fixed points), A214417 (inverse).

import Data.Bits ((.|.), (.&.))
a105027 n = foldl (.|.) 0 $ zipWith (.&.)
                  a000079_list $ enumFromTo (n + 1 - a070939 n) n
-- Reinhard Zumkeller, Jul 21 2012

block[k_] := Module[{t}, t = Table[PadLeft[IntegerDigits[n, 2], k+1], {n, 2^(k-1), 2^(k+1)-1}]; Table[FromDigits[Table[t[[n-m+1, m]], {m, 1, k+1}], 2], {n,2^(k-1)+1, 2^(k-1)+2^k}]]; block[0] = {0, 1}; Table[block[k], {k, 0, 6}] // Flatten (* Jean-François Alcover, Jun 30 2015 *)

apply( {A105027(n,L=exponent(n+!n))=sum(k=0,L,bitand(n+k-L,2^k))}, [0..55]) \\ M. F. Hasler, Apr 18 2022

a(2^n - 1) = A102371(n) for n > 0. - Philippe Deléham, May 10 2005

More terms from John W. Layman, Apr 07 2005

A105025 Write numbers in binary under each other; to get the next block of 2^k (k >= 0) terms of the sequence, start at 2^k, read diagonals in downward direction and convert to decimal.

Original entry on oeis.org

0, 1, 3, 2, 4, 7, 6, 5, 11, 10, 9, 12, 15, 14, 13, 8, 18, 17, 20, 23, 22, 21, 16, 27, 26, 25, 28, 31, 30, 29, 24, 19, 33, 36, 39, 38, 37, 32, 43, 42, 41, 44, 47, 46, 45, 40, 35, 50, 49, 52, 55, 54, 53, 48, 59, 58, 57, 60, 63, 62, 61, 56, 51, 34, 68, 71, 70, 69, 64, 75, 74, 73, 76

Offset: 0

N. J. A. Sloane, Apr 03 2005

This is a permutation of the nonnegative integers.

a(A214433(n)) = A105027(A214433(n)); a(A214489(n)) = A105029(A214489(n)). - Reinhard Zumkeller, Jul 21 2012

			........0
........1
.......10
.......11
......100 <- Starting here, the downward diagonals
......101 read 100, 111, 110, 101, giving the block 4, 7, 6, 5.
......110
......111
.....1000
.....1001
.....1010
.....1011
.........

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
Index entries for sequences that are permutations of the natural numbers
Index entries for sequences related to binary expansion of n

Cf. A102370, A105026.
Cf. A070939, A000079.
Cf. A105271 (fixed points), A214416 (inverse).

import Data.Bits ((.|.), (.&.))
a105025 n = foldl (.|.) 0 $ zipWith (.&.)
                  a000079_list $ reverse $ enumFromTo n (n - 1 + a070939 n)
-- Reinhard Zumkeller, Jul 21 2012

a:=proc(i,j) if j=1 and i<=16 then 0 else convert(i+15,base,2)[7-j] fi end: seq(a(i,2)*2^4+a(i+1,3)*2^3+a(i+2,4)*2^2+a(i+3,5)*2+a(i+4,6),i=1..16); # this is a Maple program (not necessarily the simplest) only for one block of (2^4) numbers # Emeric Deutsch, Apr 16 2005

numberOfBlocks = 7; bloc[n_] := Join[ Table[ IntegerDigits[k, 2], {k, 2^(n-1), 2^n-1}], Table[ Rest @ IntegerDigits[k, 2], {k, 2^n, 2^n+n}]]; Join[{0, 1}, Flatten[ Table[ Table[ Diagonal[bloc[n], k] // FromDigits[#, 2]&, {k, 0, -2^(n-1)+1, -1}], {n, 2, numberOfBlocks}]]] (* Jean-François Alcover, Nov 03 2016 *)

More terms from Emeric Deutsch, Apr 16 2005

A109681 "Sloping ternary numbers": write numbers in ternary under each other (right-justified), read diagonals in upward direction, convert to decimal.

Original entry on oeis.org

0, 1, 5, 3, 4, 8, 6, 16, 11, 9, 10, 14, 12, 13, 17, 15, 25, 20, 18, 19, 23, 21, 22, 26, 51, 34, 29, 27, 28, 32, 30, 31, 35, 33, 43, 38, 36, 37, 41, 39, 40, 44, 42, 52, 47, 45, 46, 50, 48, 49, 53, 78, 61, 56, 54, 55, 59, 57, 58, 62, 60, 70, 65, 63, 64, 68, 66

Offset: 0

Philippe Deléham, Aug 08 2005

All terms are distinct, but certain terms (see A109682) are missing.

For the terms 3^k-1 (all 2's in ternary), the diagonal is not started at the leading 2, but at the leading 1 of the following term. - Georg Fischer, Mar 13 2020

			number diagonal decimal
    0      0     0
    1      1     1
    2     12     5
   10     10     3
   11     11     4
   12     22     8
   20     20     6
   21    121    16
   22    102    11
  100    100     9
  101    101    10
  102    112    14
  110    110    12
  11.    ...   ...
  1.
  .

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Georg Fischer, Perl program

Cf. A109682 (complement), A109683 (ternary version), A109684.
Cf. A102370 (base 2), A325644 (base 4), A325645 (base 5), A325692 (base 6), A325693 (base 7), A325805 (base 8), A325829 (base 9), A103205 (base 10).
Cf. A030341.

a109681 n = a109681_list !! n
a109681_list = map (foldr (\d v -> 3 * v + d) 0) $ f a030341_tabf where
   f vss = (g 0 vss) : f (tail vss)
   g k (ws:wss) = if k < length ws then ws !! k : g (k + 1) wss else []
-- Reinhard Zumkeller, Nov 19 2013

t:= (n, i)-> (d-> `if`(i=0, d, t(m, i-1)))(irem(n, 3, 'm')):
b:= (n, i)-> `if`(3^i>n, 0, t(n,i) +3*b(n+1, i+1)):
a:= n-> b(n, 0):
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 13 2020

Perl
```
Cf. link.
```

Conjectured g.f. and recurrence removed by Georg Fischer, Mar 13 2020

cp's OEIS Frontend

A159066 A102370(n) modulo 7 .

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A159067 A102370(n) modulo 9 .

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A159963 Lodumo_3 of A102370 (sloping binary numbers).

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A359567 Numbers k such that A102370(k) = k + 2.

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A000035 Period 2: repeat [0, 1]; a(n) = n mod 2; parity of n.

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A077957 Powers of 2 alternating with zeros.

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A062289 Numbers n such that n-th row in Pascal triangle contains an even number, i.e., A048967(n) > 0.

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A105027 Write numbers in binary under each other; to get the next block of 2^k (k >= 0) terms of the sequence, start at 2^k, read diagonals in upward direction and convert to decimal.

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