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A307096 Positive integers m such that for any positive integer k the last k bits of the binary expansion of m is not a multiple of 3. 0
1, 5, 13, 17, 29, 37, 49, 61, 65, 77, 101, 113, 125, 133, 145, 157, 193, 205, 229, 241, 253, 257, 269, 293, 305, 317, 389, 401, 413, 449, 461, 485, 497, 509, 517, 529, 541, 577, 589, 613, 625, 637, 769, 781, 805, 817, 829, 901, 913, 925, 961, 973, 997, 1009 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The number of terms less than 2^n is the n-th Fibonacci number F(n), A000045.

The number of terms between 2^(n-1) and 2^n in the sequence is the Fibonacci number F(n-2), A000045.

If 2^(n-1) <= x < 2^n, then x is in the sequence if and only if x is not divisible by 3 and x - 2^(n-1) is in the sequence. - Robert Israel, Apr 25 2019

LINKS

Table of n, a(n) for n=1..54.

FORMULA

(a(n)+1)/2 = A219608(n), the n-th odd term in A060142.

EXAMPLE

29 is 11101_2 and none of 11101_2, 1101_2, 101_2, 1_2 are divisible by 3.

MAPLE

f := n-> if(n != 0, add(2^(k-1)*`if`((n mod 2^k) mod 3 = 0, 1, 0), k = 1 .. ceil(log(n)/log(2))), 0);

ker := []; for n from 1 to 1024 do if f(n) = 0 then ker := [op(ker), n] end if end do; ker;

# Alternative:

A1:= {1}: A2:= {}:

for d from 1 to 12 do

  if d::odd then A1:= A1 union map(`+`, A2, 2^d)

  else A2:= A2 union map(`+`, A1, 2^d)

  fi

od:

sort(convert(A1 union A2, list)); # Robert Israel, Apr 25 2019

MATHEMATICA

Select[Range[10^3], Function[s, NoneTrue[Array[FromDigits[Take[s, -#], 2] &, Length@ s], Mod[#, 3] == 0 &]]@ IntegerDigits[#, 2] &] (* Michael De Vlieger, Mar 24 2019 *)

PROG

(PARI) isok(n) = {if (n % 3, my(b=binary(n)); for (k=1, #b-1, b[k] = 0; if ((fromdigits(b, 2) % 3) == 0, return (0)); ); return (1); ); return (0); } \\ Michel Marcus, Apr 24 2019

CROSSREFS

Cf. A060142, A219608, A000045.

Sequence in context: A349900 A347163 A111055 * A283391 A145016 A354155

Adjacent sequences:  A307093 A307094 A307095 * A307097 A307098 A307099

KEYWORD

easy,base,nonn

AUTHOR

John Rickert, Mar 24 2019

STATUS

approved

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Last modified August 15 02:47 EDT 2022. Contains 356122 sequences. (Running on oeis4.)