A023804 -id:A023804 - cp's OEIS frontend

A043095 Numbers with property that no two consecutive base 9 digits are equal.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82

Offset: 1

Clark Kimberling

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A000975 (base-2 analog), A031941 or A043089 (base-3 analog), A031942 or A043090 (base-4 analog), A031943 or A043091 (base-5 analog), A043092, ..., A043096 (base-6 through base-10 analog).

Cf. A023804 (subsequence).

isA043095 := proc(n)
    dgs := convert(n,base,9) ;
    for i from 2 to nops(dgs) do
        if op(i,dgs) = op(i-1,dgs) then
            return false;
        end if;
    end do:
    true ;
end proc:
A043095 := proc(n)
    option remember;
    if n =1 then
        0;
    else
        for a from procname(n-1)+1 do
            if isA043095(a) then
                return a;
            end if;
        end do;
    end if;
end proc:
seq(A043095(n),n=1..120) ; # R. J. Mathar, Dec 28 2023

Select[Range[0,100],!MemberQ[Flatten[Differences/@Partition[ IntegerDigits[ #,9],2,1]],0]&] (* Harvey P. Dale, Apr 05 2014 *)

isok(n) = {my(d = digits(n, 9)); for (i=2, #d, if (d[i] == d[i-1], return (0));); return (1);} \\ Michel Marcus, Oct 11 2017

A342851 Remove duplicates in the decimal digit-reversal of n.

Original entry on oeis.org

Offset: 1

Michael De Vlieger, Mar 24 2021

Primitive terms in A004086.
Corresponds with A023804 for 1 <= n <= 73. The term 81 in this sequence is "100" in base 9, in which 2 digits are the same, therefore 81 does not appear in A023804.
0 plus integers that are not a multiple of 10. - Chai Wah Wu, Mar 25 2021
Differs "in substance" from A209931, because e.g. this sequence contains 214 and 214 is not in A209931 (because 107|214 and 107 contains a zero). - R. J. Mathar, Jul 29 2021
Differs from the finite sequence A023804. - R. J. Mathar, Jul 07 2023

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding Structure in Sequences of Real Numbers via Graph Theory: a Problem List, arXiv:2012.04625 [math.CO], 2020.

Cf. A004086. Essentially the same as A067251.

Mathematica
```
Union@ IntegerReverse[Range[0, 100]]
```

A342851_list = [d for d in range(10**3) if d == 0 or d % 10] # Chai Wah Wu, Mar 25 2021

A367733 Numbers k such that the sum of digits of k is equal to the sum of digits of k+9.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 101

Offset: 1

Julia Zimmerman, Nov 28 2023

Numbers k which end in the digits ...xy with x!=9 and y!=0.
Differs from A052382, as there are terms with 0 here, the first being a(82)=101. First differs from A067251 at a(82)=101, A067251(82)=91. Similarly to A067251, A209931 includes 91-99 as terms whereas they are not in this sequence. A043095(1)=0 and A023804(1)=0 whereas 0 is not a term in this sequence (there are additional differences, such as the term that comes after 89 in A023804 and A043095 being 99).
This sequence is defined as follows: |digsum(k + seed) - digsum(k)| = r where digsum is the digital sum (A007953), with seed = 9 and r = 0.
The way this sequence looks has to do with using base 10: if you choose 8 as a seed and 1 as the sought difference (r), or 7 as a seed and 2 as the sought difference, you will get similar long, full sequences. However if you choose 8 as a seed and 0 as the sought difference, you'll get no terms.

			For k=3, 3 + 9 = 12. Sum of 1 + 2 = 3. Since the sum of the digits in 3 and the sum of the digits in 12 are the same, 3 is a term of the sequence.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Cf. A007953.

Select[Range[100], Equal @@ Plus @@@ IntegerDigits[{#, # + 9}] &] (* Amiram Eldar, Nov 28 2023 *)

is(n) = sumdigits(n) == sumdigits(n+9) \\ David A. Corneth, Nov 28 2023

def A367733(n): return n + (n-1)//9 + ((n-1)//81)*10

a(n) = n + floor((n-1)/9) + floor((n-1)/81)*10.

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A043095 Numbers with property that no two consecutive base 9 digits are equal.

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A342851 Remove duplicates in the decimal digit-reversal of n.

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A367733 Numbers k such that the sum of digits of k is equal to the sum of digits of k+9.

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