A007092 -id:A007092 - cp's OEIS frontend

A102677 Number of digits >= 6 in decimal representation of n.

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

Offset: 0

N. J. A. Sloane, Feb 03 2005

a(n) = 0 iff n is in A007092 (numbers in base 6). - Bernard Schott, Feb 02 2023

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Cf. A007092, A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums see A102678.

Cf. A000120, A000788, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=6 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n),n=0..116); # Emeric Deutsch, Feb 23 2005

Table[Total@ Take[Most@ DigitCount@ n, -4], {n, 0, 104}] (* Michael De Vlieger, Aug 17 2017 *)

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = Sum_{j=1..m+1} (floor(n/10^j + 2/5) - floor(n/10^j)), where m = floor(log_10(n)).
G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(6*10^j) - x^(10*10^j))/(1-x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 23 2005

A309957 Product of digits of (n written in base 6).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 2, 4, 6, 8, 10, 0, 3, 6, 9, 12, 15, 0, 4, 8, 12, 16, 20, 0, 5, 10, 15, 20, 25, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 0, 2, 4, 6, 8, 10, 0, 3, 6, 9, 12, 15, 0, 4, 8, 12, 16, 20, 0, 5, 10, 15, 20, 25, 0, 0, 0, 0, 0, 0, 0, 2, 4, 6, 8, 10, 0, 4, 8, 12, 16, 20, 0, 6, 12, 18, 24, 30, 0, 8, 16, 24, 32

Offset: 0

Ilya Gutkovskiy, Aug 24 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A007092, A007954, A053827.

[0] cat [&*Intseq(n,6):n in [1..100]]; // Marius A. Burtea, Aug 25 2019

seq(convert(convert(n,base,6),`*`),n=0..100); # Robert Israel, Aug 24 2019

Table[Times @@ IntegerDigits[n, 6], {n, 0, 100}]

G.f. A(x) satisfies: A(x) = x * (1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4) * (1 + A(x^6)).

A353106 Base-6 representation of A007908(n).

Original entry on oeis.org

1, 20, 323, 5414, 133053, 2351320, 42243331, 1120335530, 20130035113, 5401014424514, 2343052550252003, 1114323133240053240, 321321022332303252301, 132140014431255340214310, 42015444551405453142112503

Offset: 1

Seiichi Manyama, Apr 23 2022

Seiichi Manyama, Table of n, a(n) for n = 1..295

Cf. A007908, A050926, A097580, A097582, A097583, A353104, A353105, A353107.

Cf. A007092.

def A(k, n)
  (1..n).map{|i| (1..i).to_a.join.to_i.to_s(k).to_i}
end
p A(6, 20)

a(n) = A007092(A007908(n)).

A382416 Numbers with at least one zero in their base-6 representation.

Original entry on oeis.org

0, 6, 12, 18, 24, 30, 36, 37, 38, 39, 40, 41, 42, 48, 54, 60, 66, 72, 73, 74, 75, 76, 77, 78, 84, 90, 96, 102, 108, 109, 110, 111, 112, 113, 114, 120, 126, 132, 138, 144, 145, 146, 147, 148, 149, 150, 156, 162, 168, 174, 180, 181, 182, 183, 184, 185, 186, 192, 198

Offset: 1

Paolo Xausa, Mar 25 2025

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. analogous sequences in other bases: A062289 (base 2), A081605 (base 3), A196032 (base 4), A382415 (base 5), A382413 (base 7), A382417 (base 8), A382418 (base 9), A011540 (base 10).

Cf. A007092, A043369, A248910 (complement).

Select[Range[0, 200], DigitCount[#, 6, 0] > 0 &]

A037398 Numbers k such that every base-6 digit of k is a base-7 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 14, 21, 28, 35, 43, 68, 79, 86, 122, 123, 129, 165, 172, 208, 215, 246, 252, 260, 361, 373, 397, 425, 427, 431, 444, 445, 446, 469, 475, 476, 479, 481, 482, 504, 513, 520, 527, 556, 562, 583, 625, 696, 738, 756

Offset: 1

Clark Kimberling

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

Cf. A007092, A007093.

Cf. A037399, A037400, A037401.

import Data.List ((\\), nub)
a037398 n = a037398_list !! (n-1)
a037398_list = filter f [1..] where
   f x = null $ nub (ds 6 x) \\ nub (ds 7 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

A037400 Numbers k such that every base-6 digit of k is a base-9 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 5, 21, 104, 108, 115, 129, 194, 212, 215, 252, 259, 271, 280, 352, 370, 388, 417, 504, 651, 756, 757, 758, 759, 760, 761, 762, 763, 777, 913, 922, 928, 932, 949, 976, 994, 1008, 1015, 1030, 1076, 1137, 1147, 1151, 1152

Offset: 1

Clark Kimberling

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

Cf. A007092, A007095.

Cf. A037398, A037399, A037401.

import Data.List ((\\), nub)
a037400 n = a037400_list !! (n-1)
a037400_list = filter f [1..] where
   f x = null $ nub (ds 6 x) \\ nub (ds 9 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

A043280 Maximal run length in base 6 representation of n.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling

Winston de Greef, Table of n, a(n) for n = 1..10000

Cf. A007092.

Cf. A043276-A043290 for base-2 to base-16 analogs.

A043280[n_]:=Max[Map[Length,Split[IntegerDigits[n,6]]]];Array[A043280,100] (* Paolo Xausa, Sep 27 2023 *)

A043280(n, b=6)={my(m,c=1); while(n>0, n%b==(n\=b)%b&&c++&&next; m=max(m, c); c=1); m} \\ M. F. Hasler, Jul 23 2013

A083900 Number of divisors of n with largest digit <= 5 (base 10).

Original entry on oeis.org

1, 2, 2, 3, 2, 3, 1, 3, 2, 4, 2, 5, 2, 3, 4, 3, 1, 3, 1, 6, 3, 4, 2, 6, 3, 3, 2, 4, 1, 7, 2, 4, 4, 3, 3, 5, 1, 2, 3, 7, 2, 6, 2, 6, 5, 3, 1, 6, 1, 6, 3, 5, 2, 4, 4, 4, 2, 2, 1, 10, 1, 3, 3, 4, 3, 6, 1, 4, 3, 6, 1, 6, 1, 2, 5, 3, 2, 4, 1, 7, 2, 3, 1, 8, 2, 3, 2, 6, 1, 8, 2, 4, 3, 2, 2, 7, 1, 3, 4, 9, 2, 6, 2, 6, 7

Offset: 1

Reinhard Zumkeller, May 08 2003

Cf. A054055, A000005, A007092, A083892, A083893, A083899, A083901.

Table[Count[Divisors[n],?(Max[IntegerDigits[#]]<6&)],{n,110}] (* _Harvey P. Dale, Feb 02 2015 *)

a(n) = A083899(n) + A083892(n) = A083901(n) - A083893(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A007092(k) = 5.25448032967060504709... . - Amiram Eldar, Jan 04 2024

A127113 n! in base 6.

Original entry on oeis.org

1, 1, 2, 10, 40, 320, 3200, 35200, 510400, 11440000, 205440000, 3543320000, 115310400000, 2505522400000, 104014341200000, 2440423132000000, 112255444052000000, 3300252314304000000, 143012413513200000000, 5313433311353200000000, 302523154413030400000000

Offset: 0

Artur Jasinski, Jan 05 2007

Cf. A127109, A127110, A036603, A127112, A127113, A127114, A127115, A127116.

FromDigits[IntegerDigits[#,6]]&/@(Range[0,30]!) (* Harvey P. Dale, Jun 18 2019 *)

a(n) = A007092(A000142(n)). - R. J. Mathar, Jun 09 2020

More terms from Harvey P. Dale, Jun 18 2019

A032545 Integer part of decimal 'base-6 looking' numbers divided by their actual base-6 values, rounded down.

Original entry on oeis.org

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

Offset: 1

Patrick De Geest, Apr 15 1998

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A007092, A032546, A032547.

cp's OEIS Frontend

A102677 Number of digits >= 6 in decimal representation of n.

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A309957 Product of digits of (n written in base 6).

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Magma

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A353106 Base-6 representation of A007908(n).

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A382416 Numbers with at least one zero in their base-6 representation.

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A037398 Numbers k such that every base-6 digit of k is a base-7 digit of k.

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Haskell

A037400 Numbers k such that every base-6 digit of k is a base-9 digit of k.

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A043280 Maximal run length in base 6 representation of n.

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A083900 Number of divisors of n with largest digit <= 5 (base 10).

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A127113 n! in base 6.

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