A174657 -id:A174657 - cp's OEIS frontend

A174658 Balanced ternary numbers with equal count of negative trits and positive trits.

0, 2, 6, 8, 16, 18, 20, 24, 26, 32, 46, 48, 52, 54, 56, 60, 62, 70, 72, 74, 78, 80, 86, 96, 98, 104, 130, 136, 138, 142, 144, 146, 154, 156, 160, 162, 164, 168, 170, 178, 180, 182, 186, 188, 194, 208, 210, 214, 216, 218, 222, 224, 232, 234, 236, 240, 242, 248, 258

Offset: 1

Daniel Forgues, Mar 26 2010

Numbers for which the sum of trits is zero.

Daniel Forgues, Table of n, a(n) for n=1..14309

Cf. A174657, A174659, A065363, A140267, A257869.

(* First run the program for A065363 to define balTernDigits *) A174658 = Select[Range[0, 299], Plus@@balTernDigits[#] == 0 &] (* Alonso del Arte, Feb 24 2011 *)

def a(n):
    s=0
    x=0
    while n>0:
        x=n%3
        n //= 3
        if x==2:
            x=-1
            n+=1
        s+=x
    return s
print([n for n in range(301) if a(n)==0]) # Indranil Ghosh, Jun 07 2017

A174659 Numbers whose balanced ternary representation has more positive trits than negative trits.

Original entry on oeis.org

1, 3, 4, 7, 9, 10, 11, 12, 13, 19, 21, 22, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 49, 55, 57, 58, 61, 63, 64, 65, 66, 67, 73, 75, 76, 79, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 97, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 111, 112

Offset: 1

Daniel Forgues, Mar 26 2010

Numbers for which the sum of trits is positive.

Daniel Forgues, Table of n, a(n) for n=1..53007

Cf. A174657, A174658, A065363, A140267.

(* First run the program for A065363 to define balTernDigits *) Select[Range[210], Count[balTernDigits[#], -1] < Count[balTernDigits[#], 1] &] (* Alonso del Arte, Feb 26 2011 *)

def a(n):
    s=0
    x=0
    while n>0:
        x=n%3
        n//=3
        if x==2:
            x=-1
            n+=1
        s+=x
    return s
print([n for n in range(301) if a(n)>0]) # Indranil Ghosh, Jun 07 2017

a(n) < 2n. - Yifan Xie, Dec 24 2024

A334765 Numbers m such that the numbers of 1's in the binary expansion of m equals the negative sum of balanced ternary trits of m.

Original entry on oeis.org

0, 41, 68, 131, 132, 368, 384, 528, 1095, 1098, 1100, 1106, 1112, 1122, 1124, 1152, 1176, 1346, 1824, 2561, 3282, 3284, 3336, 3344, 3392, 3524, 4098, 4101, 4104, 4112, 4118, 4128, 4172, 4352, 4496, 4739, 4740, 5504, 6224, 9856, 9857, 9869, 9896, 9923, 9924

Offset: 1

Thomas König, May 10 2020

a(116) = 32770, a(117) = 32771 and a(118) = 32772 is the first time that three consecutive numbers appear in this sequence. Conjecture: There is no occurrence of four or more consecutive numbers. Tested by exhaustive search up to a(n) = 3^26. - Thomas König, Jul 19 2020

			41_10 = 1TTTT_bt = 101001_2, the sum of the digits is 1-1-1-1-1 = -3 for balanced ternary and 1+1+1 = 3 for base 2, so 41 is a term.

Thomas König, Table of n, a(n) for n = 1..30000

Aside from the first term, subsequence of A174657.

Cf. A000120, A037301, A065363, A330904.

Select[Range[0, 10^4], -Total@ If[First@ # == 0, Rest@ #, #] &[Prepend[IntegerDigits[#, 3], 0] //. {x___, y_, k_ /; k > 1, z___} :> {x, y + 1, -1, z}] == DigitCount[#, 2, 1] &] (* Michael De Vlieger, Jul 08 2020 *)

bt(n)= if (n==0, return (0)); my(d=digits(n, 3), c=1); while(c, if(d[1]==2, d=concat(0, d)); c=0; for(i=2, #d, if(d[i]==2, d[i]=-1; d[i-1]+=1; c=1))); vecsum(d); \\ A065363
isok(m) = bt(m) + hammingweight(m) == 0; \\ Michel Marcus, Jun 07 2020

Integers m such that -A065363(m) = A000120(m).

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A174658 Balanced ternary numbers with equal count of negative trits and positive trits.

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A174659 Numbers whose balanced ternary representation has more positive trits than negative trits.

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A334765 Numbers m such that the numbers of 1's in the binary expansion of m equals the negative sum of balanced ternary trits of m.

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