A174659 -id:A174659 - 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

A174657 Balanced ternary numbers with more negative trits than positive trits.

Original entry on oeis.org

5, 14, 15, 17, 23, 41, 42, 43, 44, 45, 47, 50, 51, 53, 59, 68, 69, 71, 77, 95, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 137, 140, 141, 143, 149, 150, 151, 152, 153, 155, 158, 159, 161, 167, 176, 177, 179, 185, 203, 204, 205, 206, 207, 209

Offset: 1

Daniel Forgues, Mar 26 2010

Numbers for which the sum of trits is negative.

Daniel Forgues, Table of n, a(n) for n=1..32685

Cf. A174658, A174659, 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

A330904 Numbers m such that the number of 1's in the binary expansion of m equals the sum of the balanced ternary trits of m.

Original entry on oeis.org

0, 1, 10, 12, 13, 34, 36, 37, 66, 67, 120, 121, 192, 193, 202, 264, 265, 272, 273, 282, 283, 354, 355, 360, 361, 514, 516, 517, 520, 526, 544, 576, 577, 688, 840, 841, 848, 849, 904, 928, 1026, 1027, 1028, 1029, 1032, 1033, 1038, 1039, 1062, 1063, 1074, 1075

Offset: 1

Thomas König, May 02 2020

If a(n) mod 6 = 0, then a(n+1) = a(n)+1.

a(41) = 1026, a(42) = 1027, a(43) = 1028 and a(44) = 1029 is the first time that four consecutive numbers appear in a(n). Conjecture: There is no occurrence of five or more consecutive numbers in a(n). Tested by exhaustive search up to 3^30. - Thomas König, Jul 19 2020

			34_10 = 11T1_bt = 10010_2, the sum of the digits is 1+1-1+1 = 2 for balanced ternary and 1+1 = 2 for base 2, so 34 is a term.

Thomas König, Table of n, a(n) for n = 1..20000
Thomas König, C program
Thomas König, Fortran program to test the conjecture that there are at most four consecutive numbers in sequence

Aside from the first term, subsequence of A174659.

Cf. A000120, A037301, A065363.

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); \\ Michel Marcus, Jun 07 2020

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

Offset corrected by Thomas König, Jul 09 2020

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

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A174657 Balanced ternary numbers with more negative trits than positive trits.

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Python

A330904 Numbers m such that the number of 1's in the binary expansion of m equals the sum of the balanced ternary trits of m.

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