A326956 Characteristic function of A228354.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences related to binary expansion of n

Example

-------------------------------------------------------------
.                  |          Compositions of k
.                  |
   n  a(n) A228354 | k = 1    2     3       4         5
-------------------------------------------------------------
.
   1   1      1          1    1+1   1+1+1   1+1+1+1   1+1+1+1+1
   2   1      2               2     2+1     2+1+1     2+1+1+1
   3   0                            1+2     1+2+1     1+2+1+1
   4   1      4                     3       3+1       3+1+1
   5   0                                    1+1+2     1+1+2+1
   6   1      6                             2+2       2+2+1
   7   0                                    1+3       1+3+1
   8   1      8                             4         4+1
   9   0                                              1+1+1+2
  10   0                                              2+1+2
  11   0                                              1+2+2
  12   1     12                                       3+2
  13   0                                              1+1+3
  14   0                                              2+3
  15   0                                              1+4
  16   1     16                                       5
...
Note that removing the compositions of k in colexicographic order that are associated to the zeros of this sequence so we have the partitions of k in the same order.

Prog

(PARI)
isA194602(n) = if(!n, 1, if(!(n%2), 0, my(prl=0, rl=0); while(n, if(0==(n%2), if((prl && rl>prl)||0==(n%4), return(0)); prl=rl; rl=0, rl++); n >>= 1); ((0==prl)||(rl<=prl)))); \\ See A194602.
A326956(n) = isA194602(n-1); \\ Antti Karttunen, Dec 06 2021

Crossrefs

Cf. A000041, A011782, A187219, A194602, A211992, A228354, A228525, A228720.

Sequence in context: A343999 A344438 A322585 * A341629 A365429 A322860

Adjacent sequences: A326953 A326954 A326955 * A326957 A326958 A326959

Keyword

nonn

Author

Omar E. Pol, Sep 14 2019

Extensions

Data section extended up to 120 terms by Antti Karttunen, Dec 06 2021

Status

approved