A277966 -id:A277966 - cp's OEIS frontend

A083891 Number of divisors of n with largest digit = 4 (base 10).

0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 1, 2, 1, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0

Offset: 1

Reinhard Zumkeller, May 08 2003

			n=120, 3 of the 16 divisors of 120 have largest digit=4: {4,24,40}, therefore a(120)=3.

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

Cf. A054055, A000005, A083899, A277966.

ld4:= n -> max(convert(n,base,10)) = 4:
f:= n -> nops(select(ld4,numtheory:-divisors(n))):
map(f, [$1..100]); # Robert Israel, May 02 2019

Table[Count[Divisors[n],?(Max[IntegerDigits[#]]==4&)],{n,110}] (* _Harvey P. Dale, Feb 19 2016 *)

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083892(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n) = A083899(n) - A083898(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A277966(k) = 0.98827280431174433126... . - Amiram Eldar, Jan 04 2024

A277948 Squares whose largest decimal digit is 4.

Original entry on oeis.org

4, 144, 324, 400, 441, 1024, 1444, 2304, 2401, 10404, 14400, 23104, 32041, 32400, 33124, 40000, 40401, 44100, 101124, 102400, 103041, 110224, 114244, 121104, 131044, 144400, 203401, 204304, 213444, 230400, 232324, 240100, 300304, 301401, 421201, 1004004

Offset: 1

Colin Barker, Nov 05 2016

A subsequence of A158082, in turn a subsequence of A000290.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A000290 (the squares).
Cf. A277961 (square roots of these terms).
Cf. A277946, A277947, A295015, ..., A295019 (analog for largest digit = 2, 3, 5, ..., 9).
Cf. A058412, A058411, ..., A058474 and A136808, A136809, ..., A137147 for other restrictions on digits of squares.

[n^2: n in [1..1000000] | Maximum(Intseq(n^2)) eq 4]; // Vincenzo Librandi, Nov 06 2016

Select[Range[1100]^2,Max[IntegerDigits[#]]==4&] (* Harvey P. Dale, Jul 01 2017 *)

L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==4, listput(L, n^2))); Vec(L)

a(n) = A277961(n)^2. - M. F. Hasler, Nov 12 2017

Intersection of A000290 and A277966. - M. F. Hasler, Nov 15 2017

A277964 Numbers whose largest decimal digit is 2.

Original entry on oeis.org

2, 12, 20, 21, 22, 102, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222, 1002, 1012, 1020, 1021, 1022, 1102, 1112, 1120, 1121, 1122, 1200, 1201, 1202, 1210, 1211, 1212, 1220, 1221, 1222, 2000, 2001, 2002, 2010, 2011, 2012, 2020, 2021, 2022

Offset: 1

Colin Barker, Nov 06 2016

Number of terms less than 10^n is 3^n-2^n, i.e., A001047(n). - Chai Wah Wu, Nov 06 2016 [extended by Felix Fröhlich, Nov 07 2016]

Numbers n such that A054055(n) = 2. - Felix Fröhlich, Nov 07 2016

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Colin Barker)

Cf. A007088, A277965, A277966.

Filtered([1..2100],n->Maximum(ListOfDigits(n))=2); # Muniru A Asiru, Mar 01 2019

N:= 6: # to get all terms of at most N digits
R:= 2: B:= {1}: C:= {1,2}:
for  d from 2 to N do B:= map(t -> (10*t,10*t+1),B);
C:= map(t -> (10*t,10*t+1,10*t+2),C);
R:= R, op(sort(convert(C minus B,list)))
od:
R; # Robert Israel, Nov 07 2016

A277964Q = Max[IntegerDigits[#]] == 2 &; Select[Range[2000], A277964Q] (* JungHwan Min, Nov 06 2016 *)

L=List(); for(n=1, 10000, if(vecmax(digits(n))==2, listput(L, n))); Vec(L)

A277965 Numbers whose largest decimal digit is 3.

Original entry on oeis.org

3, 13, 23, 30, 31, 32, 33, 103, 113, 123, 130, 131, 132, 133, 203, 213, 223, 230, 231, 232, 233, 300, 301, 302, 303, 310, 311, 312, 313, 320, 321, 322, 323, 330, 331, 332, 333, 1003, 1013, 1023, 1030, 1031, 1032, 1033, 1103, 1113, 1123, 1130, 1131, 1132

Offset: 1

Colin Barker, Nov 06 2016

Number of terms less than 10^n is 4^n - 3^n. - Chai Wah Wu, Nov 06 2016

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Colin Barker)

Cf. A007088, A277964, A277966.
Cf. A005061 (4^n - 3^n).
Cf. A106099 (subsequence of primes).

Filtered([1..450],n->Maximum(ListOfDigits(n))=3); # Muniru A Asiru, Mar 01 2019

A277965Q = Max[IntegerDigits[#]] == 3 &; Select[Range[1200], A277965Q] (* JungHwan Min, Nov 06 2016 *)

L=List(); for(n=1, 10000, if(vecmax(digits(n))==3, listput(L, n))); Vec(L)

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

cp's OEIS Frontend

A083891 Number of divisors of n with largest digit = 4 (base 10).

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A277948 Squares whose largest decimal digit is 4.

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A277964 Numbers whose largest decimal digit is 2.

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A277965 Numbers whose largest decimal digit is 3.

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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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