A190592 -id:A190592 - cp's OEIS frontend

A190941 Partial sums of A190592.

0, 1, 3, 4, 5, 7, 9, 11, 13, 14, 15, 17, 18, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 46, 47, 49, 50, 51, 53, 55, 57, 59, 60, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 146, 147, 149, 150, 151, 153, 155, 157, 159, 160, 161, 163, 164, 165, 167, 169, 171, 173, 175, 177, 179, 181, 183, 185

Offset: 0

Jonathan Vos Post, May 24 2011

Compare with obvious base-2 analog. What is the general base-k formula?

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Accumulate@ Array[Max@ IntegerDigits[#, 3] &, 105, 0] (* Michael De Vlieger, Feb 15 2020 *)

a(n) = Sum_{i=0..n} (maximal digit in base-3 expansion of i).

a(n) = 3n + O(n^0.631). - Charles R Greathouse IV, Aug 21 2011

A054055 Largest digit of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 2, 2, 3, 4, 5, 6, 7, 8, 9, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9, 4, 4, 4, 4, 4, 5, 6, 7, 8, 9, 5, 5, 5, 5, 5, 5, 6, 7, 8, 9, 6, 6, 6, 6, 6, 6, 6, 7, 8, 9, 7, 7, 7, 7, 7, 7, 7, 7, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 2, 3, 4

Offset: 0

Henry Bottomley, Apr 29 2000

A095815(n) = n + a(n). - Reinhard Zumkeller, Aug 23 2011
a(A007088(n)) = 1, n > 0; a(A136399(n)) > 1. - Reinhard Zumkeller, Apr 25 2012
a(n) = 9 for almost all n. Sum_{n < x} a(n) = 9x + O(.956^x). - Charles R Greathouse IV, Oct 02 2013

			a(12)=2 because 1 < 2.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

For bases 3 through 12 see A190592, A190593, A190594, A190595, A190596, A190597, A190598, A054055, A190599, A190600.

Cf. A054054.

a054055 = f 0 where
   f m x | x <= 9 = max m x
         | otherwise = f (max m d) x' where (x',d) = divMod x 10
-- Reinhard Zumkeller, Jun 20 2012, May 14 2011

[n eq 0 select 0 else Maximum(Intseq(n)): n in [0..104]]; // Bruno Berselli, Aug 24 2011

[seq(max(convert(n,base,10)),n=0..120)];

f[n_] := Sort[IntegerDigits[n]][[-1]]; Array[f, 105, 0] (* Alonso del Arte, May 14 2011 *) (* and revised by Robert G. Wilson v, Aug 24 2011 *)
Max/@IntegerDigits[Range[0,110]] (* Harvey P. Dale, Apr 17 2016 *)

a(n)=vecmax(eval(Vec(Str(n)))) \\ Charles R Greathouse IV, Jun 16 2011

a(n)=vecmax(digits(n)) \\ Charles R Greathouse IV, Oct 02 2013

def A054055(n): return max(int(d) for d in str(n)) # Chai Wah Wu, Jun 06 2022

A037897 (Greatest base 3 digit of n)-(least base 3 digit of n).

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 0, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 0, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 0, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 0, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Clark Kimberling

Antti Karttunen, Table of n, a(n) for n = 1..19683

Cf. A007089, A043530, A190592, A290825.

A037897 := proc(n)
    local dgs ;
    dgs := convert(n,base,3);
    max(op(dgs))-min(op(dgs)) ;
end proc: # R. J. Mathar, Oct 19 2015

A037897(n) = (vecmax(digits(n,3)) - vecmin(digits(n,3))); \\ Antti Karttunen, Aug 11 2017

a(n) = A190592(n) - A290825(n). - Antti Karttunen, Aug 12 2017

Offset corrected by R. J. Mathar, Oct 19 2015

More terms from Antti Karttunen, Aug 11 2017

A290825 Least base-3 digit of n.

Original entry on oeis.org

0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Robert Israel, Aug 11 2017

			11 = 102_3 so a(11)=0.

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A002264, A010872, A024023, A037897, A190592.

Maple
```
seq(min(convert(n,base,3)),n=0..100);
```

Table[Min[IntegerDigits[n,3]],{n,0,120}] (* Harvey P. Dale, Dec 19 2017 *)

a(n) = if (n==0, 0, vecmin(digits(n, 3))); \\ Michel Marcus, Aug 12 2017

a(n) = 2 if and only if n > 0 is in A024023.
a(n) = 0 if n is divisible by 3.
a(n) = min(A010872(n), a(A002264(n))).

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A190941 Partial sums of A190592.

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A054055 Largest digit of n.

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A037897 (Greatest base 3 digit of n)-(least base 3 digit of n).

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A290825 Least base-3 digit of n.

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