A054055 -id:A054055 - cp's OEIS frontend

A115300 Greatest digit of n * least digit of n.

1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8

Offset: 1

Rick L. Shepherd, Jan 20 2006

a(101) = 0 and A111707(101) = 1, but all previous terms match.

a(n) = A169669(n) for n <= 100.

			a(3) = 3 * 3 = 9, a(232) = 3 * 2 = 6, a(1889009898) = 9 * 0 = 0.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A037904 (greatest-least), A115299 (greatest+least), A111707.

Cf. A054054, A054055, A169669.

a115300 n = a054054 n * a054055 n  -- Reinhard Zumkeller, Apr 29 2015

Array[Max[#] * Min[#] &@ IntegerDigits[#] &, 81] (* James C. McMahon, Aug 18 2024 *)

a(n) = my(d=digits(n)); vecmin(d)*vecmax(d); \\ Michel Marcus, Aug 18 2024

def a(n): d = list(map(int, str(n))); return max(d) * min(d)
print([a(n) for n in range(1, 82)]) # Michael S. Branicky, Dec 12 2023

a(n) = A054054(n)*A054055(n). - Reinhard Zumkeller, Apr 29 2015

A136399 Numbers having in their decimal representation at least one digit greater than 1.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

Offset: 1

Reinhard Zumkeller, Dec 30 2007

A054055(a(n)) > 1;

Complement of A007088; A064770(a(n)) <> a(n).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007088, A054055, A064770.

a136399 n = a136399_list !! (n-1)
a136399_list = filter (any (> '1') . show) [0..]
-- Reinhard Zumkeller, Apr 25 2012

Select[Range[100], Max[IntegerDigits[#]] > 1 &] (* Paolo Xausa, Oct 30 2024 *)

def A136399(n):
    def f(x):
        s = str(x)
        for i in range(l:=len(s)):
            if s[i]>'1':
                break
        else:
            return n+int(s,2)
        return n+int(s[:i]+'1'*(l-i),2)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Oct 16 2024

def ok(n): return any(d > '1' for d in str(n))
print([k for k in range(76) if ok(k)]) # Michael S. Branicky, Oct 29 2024

A190592 Maximal digit in base-3 expansion of n.

Original entry on oeis.org

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, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 0

N. J. A. Sloane, May 13 2011, based on a suggestion from Marc LeBrun

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

Cf. A007089, A054055, A037897.

Maple
```
[seq(max(convert(n,base,3)),n=0..120)];
```

Join[{0}, gl[n_] := Module[{idn = IntegerDigits[n, 3]}, Max[idn]]; Array[gl,100]] (* Vincenzo Librandi, Aug 12 2017 *)

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

a(n) = 2 if n == 2 (mod 3), a(1)=1, otherwise a(n) = a(floor(n/3)). - Robert Israel, Aug 11 2017

a(n) = A054055(A007089(n)). - Felix Fröhlich, Aug 13 2017

A283608 Numbers whose largest decimal digit is 5.

Original entry on oeis.org

5, 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 105, 115, 125, 135, 145, 150, 151, 152, 153, 154, 155, 205, 215, 225, 235, 245, 250, 251, 252, 253, 254, 255, 305, 315, 325, 335, 345, 350, 351, 352, 353, 354, 355, 405, 415, 425, 435, 445, 450, 451, 452, 453, 454

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 5.
Number of terms less than 10^n is 6^n - 5^n.
Subsequence of A011535. - David A. Corneth, Mar 25 2017
Prime terms are in A106097.

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Cf. A011535, A054055, A106097.

Cf. Sequences of numbers whose largest decimal digit is k (for k = 1..9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), this sequence (k = 5), A283609 (k = 6), A283610 (k = 7), A283611 (k = 8), A011539 (k = 9).

Filtered([1..500],n->Maximum(ListOfDigits(n))=5); # Muniru A Asiru, Feb 27 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 5];

Select[Range[1000], Max[IntegerDigits[#]] == 5 &] (* Giovanni Resta, Mar 19 2017 *)

for(n=1, 500, if(vecmax(digits(n))==5, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

nxt(n) = {my(d = digits(n), i, j=0, t=0); forstep(i=#d,1,-1, if(d[i]!=5, j=i; break)); if(j>0, d[j]++; if(d[j]==5, for(k=j+1,#d,d[k]=0)); if(j<#d && d[j+1]==5, for(k=j+1,#d-1,d[k]=0)); for(k=1,j-1, if(d[k]==5,for(i=j+1, #d, d[i] = 0);break)), d = vector(#d+1); d[1]=1; d[#d]=5);sum(i=1, #d, d[i]*10^(#d-i))} \\ David A. Corneth, Mar 25 2017

from sympy.ntheory.factor_ import digits
print([n for n in range(1, 501) if max(digits(n)[1:])==5]) # Indranil Ghosh, Mar 19 2017

A283609 Numbers whose largest decimal digit is 6.

Original entry on oeis.org

6, 16, 26, 36, 46, 56, 60, 61, 62, 63, 64, 65, 66, 106, 116, 126, 136, 146, 156, 160, 161, 162, 163, 164, 165, 166, 206, 216, 226, 236, 246, 256, 260, 261, 262, 263, 264, 265, 266, 306, 316, 326, 336, 346, 356, 360, 361, 362, 363, 364, 365, 366, 406, 416, 426

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 6.
Number of terms less than 10^n is 7^n - 6^n.
Prime terms are in A106096.

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Cf. A054055, A106096.

Cf. Sequences of numbers whose largest decimal digit is k (for k = 1..9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), A283608 (k = 5), this sequence (k = 6), A283610 (k = 7), A283611 (k = 8), A011539 (k = 9).

Filtered([1..500],n->Maximum(ListOfDigits(n))=6); # Muniru A Asiru, Mar 01 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 6]

Select[Range[1000], Max[IntegerDigits[#]] == 6 &] (* Giovanni Resta, Mar 19 2017 *)

for(n=1, 500, if(vecmax(digits(n))==6, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

from sympy.ntheory.factor_ import digits
print([n for n in range(1, 501) if max(digits(n)[1:])==6]) # Indranil Ghosh, Mar 19 2017

A283610 Numbers n whose largest decimal digit is 7.

Original entry on oeis.org

7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 107, 117, 127, 137, 147, 157, 167, 170, 171, 172, 173, 174, 175, 176, 177, 207, 217, 227, 237, 247, 257, 267, 270, 271, 272, 273, 274, 275, 276, 277, 307, 317, 327, 337, 347, 357, 367, 370, 371, 372

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 7.
Number of terms less than 10^n is 8^n - 7^n.
Prime terms are in A106095.

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Cf. A054055, A106095.

Cf. Sequences of numbers n whose largest decimal digit is k (for k = 1 - 9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), A283608 (k = 5), A283609 (k = 6), this sequence (k = 7), A283611 (k = 8), A011539 (k = 9).

Filtered([1..380],n->Maximum(ListOfDigits(n))=7); # Muniru A Asiru, Feb 27 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 7]

Select[Range[1000], Max[IntegerDigits[#]] == 7 &] (* Giovanni Resta, Mar 19 2017 *)

for(n=1, 500, if(vecmax(digits(n))==7, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

from sympy.ntheory.factor_ import digits
[n for n in range(1, 401) if max(digits(n)[1:]) == 7]  # Indranil Ghosh, Mar 19 2017

A283611 Numbers whose largest decimal digit is 8.

Original entry on oeis.org

8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 108, 118, 128, 138, 148, 158, 168, 178, 180, 181, 182, 183, 184, 185, 186, 187, 188, 208, 218, 228, 238, 248, 258, 268, 278, 280, 281, 282, 283, 284, 285, 286, 287, 288, 308, 318, 328, 338, 348

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 8.
Number of terms less than 10^n is 9^n - 8^n.
Prime terms are in A106094.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. Sequences of numbers whose largest decimal digit is k (for k = 1..9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), A283608 (k = 5), A283609 (k = 6), A283610 (k = 7), this sequence (k = 8), A011539 (k = 9).

Filtered([1..400],n->Maximum(ListOfDigits(n))=8); # Muniru A Asiru, Mar 01 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 8]

f:= proc(n) local L;
  L:= convert(n,base,9);
  if not has(L,8) then return NULL fi;
  add(L[i]*10^(i-1),i=1..nops(L))
end proc:
map(f, [$8..1000]); # Robert Israel, Mar 27 2017

Select[Range@ 350, Max@ IntegerDigits@ # == 8 &] (* Michael De Vlieger, Mar 25 2017 *)

isok(n) = vecmax(digits(n)) == 8; \\ Michel Marcus, Mar 25 2017

A041000 If decimal expansion of n-th prime is x1 x2 ... xk, sort the xi into nonincreasing order, y1 y2 ... yk; then a(n) = |y1-y2-y3...-yk|.

Original entry on oeis.org

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

Offset: 1

Felice Russo

			a(397)=|9-7-3|=1.

Cf. A040164, A007953, A054055.

der[n_]:=Module[{c=Reverse[Sort[IntegerDigits[n]]]},Abs[First[c]-Total[Rest[c]]]]; der/@Prime[Range[110]] (* Harvey P. Dale, Aug 15 2012 *)

a(n) = |A007953(n)-2*A054055(n)|. [Charles R Greathouse IV, May 07 2011]

More terms from Michel ten Voorde

A071204 Numbers which are multiples of their largest digit (decimal notation).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 35, 36, 40, 44, 45, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 101, 102, 104, 105, 110, 111, 112, 115, 120, 122, 123, 124, 125, 126, 128, 132, 135, 140, 144, 145

Offset: 1

Reinhard Zumkeller, May 16 2002

			15 is a term since 15/5 = 3.
16 is not a term because 16/6 = 2.66666666...

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A071203, A071205, A071206, a(n) mod A054055(n) = 0.

Select[Range[200], Divisible[#, Sort[IntegerDigits[#]][[-1]]] &] (* Alonso del Arte, Sep 09 2017 *)

isok(n) = (n % vecmax(digits(n))) == 0; \\ Michel Marcus, Sep 11 2017

A072543 Numbers whose largest decimal digit is also the initial digit.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 30, 31, 32, 33, 40, 41, 42, 43, 44, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 110, 111, 200, 201

Offset: 1

Reinhard Zumkeller, Aug 04 2002

A054055(a(n)) = A000030(a(n));

the sequence differs from A009996, A032873 and A032907: a(66)=101 is not in A009996, a(67)=110 is not in A032873 and a(65)=100 is not in A032907.

			a(10^ 1) = 9
a(10^ 2) = 411
a(10^ 3) = 6216
a(10^ 4) = 73474
a(10^ 5) = 813826
a(10^ 6) = 8512170
a(10^ 7) = 88368780
a(10^ 8) = 911960211
a(10^ 9) = 9237655227
a(10^10) = 93323313303

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A072544.

a072543 n = a072543_list !! (n-1)
a072543_list = [x | x <- [0..], a054055 x == a000030 x]
-- Reinhard Zumkeller, Apr 25 2012

for i from 1 to 10 do A[i]:= i-1 od:
count:= 10:
for i from 1 to 9 do P[i]:= [seq([j],j=0..i)]; od:
for d from 2 to 4 do
  for x from 1 to 9 do
    for p in P[x] do
      count:= count+1;
      A[count]:= add(p[k]*10^(k-1),k=1..d-1) + x*10^(d-1);
    od:
    P[x]:= [seq(seq([op(v),t], v=P[x]),t=0..x)];
  od
od:
seq(A[i],i=1..count); # Robert Israel, Feb 01 2015

Select[Range[0,250],Max[IntegerDigits[#]]==First[IntegerDigits[#]]&] (* Harvey P. Dale, Apr 28 2016 *)

is(n)=n=digits(n); !#n || n[1]==vecmax(n) \\ Charles R Greathouse IV, Jan 02 2014

a(n)={d = 0; r = 1; s = 0; i = 0; if(n == 1, 0, n-=2; while(n > sum(i=0, 9,(i+1)^d), n-=sum(i=0, 9, (i+1)^d); n++; d++); while(n >= (r+1)^d, n -= (r+1)^d; r++);s = r * 10^d; while(n, s += 10^i*(n%(r+1)); n \= (r+1); i++));s } \\ David A. Corneth, Jan 31 2015

Offset corrected by Reinhard Zumkeller, Apr 25 2012

cp's OEIS Frontend

A115300 Greatest digit of n * least digit of n.

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A136399 Numbers having in their decimal representation at least one digit greater than 1.

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A190592 Maximal digit in base-3 expansion of n.

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A283608 Numbers whose largest decimal digit is 5.

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A283609 Numbers whose largest decimal digit is 6.

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A283610 Numbers n whose largest decimal digit is 7.

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A283611 Numbers whose largest decimal digit is 8.

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