A007094 -id:A007094 - cp's OEIS frontend

A037399 Numbers k such that every base-6 digit of k is a base-8 digit of k.

1, 2, 3, 4, 5, 28, 80, 85, 86, 98, 115, 160, 172, 213, 266, 331, 345, 532, 691, 699, 705, 708, 717, 720, 727, 763, 765, 792, 799, 811, 819, 835, 851, 859, 861, 863, 864, 900, 916, 928, 1036, 1061, 1068, 1085, 1093, 1128, 1129, 1130

Offset: 1

Clark Kimberling

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

Cf. A007092, A007094.

Cf. A037398, A037400, A037401.

import Data.List ((\\), nub)
a037399 n = a037399_list !! (n-1)
a037399_list = filter f [1..] where
   f x = null $ nub (ds 6 x) \\ nub (ds 8 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

b68Q[n_]:=Module[{b6=Union[IntegerDigits[n,6]],b8=Union[IntegerDigits[ n,8]]}, And@@Table[ MemberQ[b8,b6[[i]]],{i,Length[b6]}]]; Select[Range[ 1200],b68Q] (* Harvey P. Dale, Mar 24 2012 *)

A136381 Sequence A136380 shown in octal base.

Original entry on oeis.org

30, 240, 27300, 275332400, 27624273321353000, 277524424264553332245513535524000, 27762724550512424245125524562733322130552452655353526564552130000, 277751305605652455261312526532424241366545132655245452272135533332224427213254552451226545102753535225125262712455250570562640000

Offset: 1

Antti Karttunen, Dec 29 2007

A. Karttunen, Table of n, a(n) for n = 1..10
A. Karttunen, C program for computing this sequence

Cf. A036285, A136383 (shifted two bits right), A136385.

a(n) = A007094(A136380(n)).

A136383 Sequence A136382 shown in octal base.

Original entry on oeis.org

6, 50, 5660, 57266500, 5745056664272600, 57725105055132666451322727325000, 5774565132122505051225325134566664426132512553272725535132426000, 57772261341352513254262525526505050275531226553251312456427326666445105642653132512245531220572727245225254562513252136134550000

Offset: 1

Antti Karttunen, Dec 29 2007

A. Karttunen, Table of n, a(n) for n = 1..11
A. Karttunen, C program for computing this sequence

Cf. A036285, A136381 (shifted two bits left), A136385.

a(n) = A007094(A136382(n)).

A136385 Sequence A136384 shown in octal base.

Original entry on oeis.org

4, 60, 6440, 65444600, 6506064447454400, 65231606066154444716234545546000, 6527131623634606061431546150644447033623163115454546626154744000, 65254336276263162310334631144606060326621433115461563064745544444706171303315623163471156340654545471431467134615463624150660000

Offset: 1

Antti Karttunen, Dec 29 2007

A. Karttunen, Table of n, a(n) for n = 1..10
A. Karttunen, C program for computing this sequence

Cf. A036285, A136381, A136383.

a(n) = A007094(A136384(n)).

A217009 Multiples of 7 in base 8.

Original entry on oeis.org

7, 16, 25, 34, 43, 52, 61, 70, 77, 106, 115, 124, 133, 142, 151, 160, 167, 176, 205, 214, 223, 232, 241, 250, 257, 266, 275, 304, 313, 322, 331, 340, 347, 356, 365, 374, 403, 412, 421, 430, 437, 446, 455, 464, 473, 502, 511, 520, 527, 536, 545, 554, 563

Offset: 1

Jon Perry, Sep 23 2012

Digit sum is always divisible by 7.

Reinterpreting this sequence in base 10, these are numbers of the form 9n + 7 but with all numbers containing 8s and/or 9s removed. - Alonso del Arte, Sep 23 2012

			a(10) = 106 because 7 * 10 = 70, or 1 * 8^2 + 0 * 8^1 + 6 * 8^0 = 64 + 6 = 106_8.

Cf. A216994, A216995, A216996, A216997, A216998.

Cf. A008589.

k = 7;
for (i = 1; i <= 200; i++) {
x = i * k;
document.write(x.toString(k + 1) + ", ");
}

Table[BaseForm[7*n, 8], {n, 100}] (* Alonso del Arte, Sep 23 2012 *)
Select[9*Range[0, 99] + 7, DigitCount[#, 10, 8] == 0 && DigitCount[#, 10, 9] == 0 &] (* Alonso del Arte, Sep 23 2012 *)
Table[FromDigits[IntegerDigits[7*n, 8]], {n, 100}] (* T. D. Noe, Sep 24 2012 *)

a(n) = A007094(A008589(n)). -

A382417 Numbers with at least one zero in their base-8 representation.

Original entry on oeis.org

0, 8, 16, 24, 32, 40, 48, 56, 64, 65, 66, 67, 68, 69, 70, 71, 72, 80, 88, 96, 104, 112, 120, 128, 129, 130, 131, 132, 133, 134, 135, 136, 144, 152, 160, 168, 176, 184, 192, 193, 194, 195, 196, 197, 198, 199, 200, 208, 216, 224, 232, 240, 248, 256, 257, 258, 259, 260

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), A382416 (base 6), A382413 (base 7), A382418 (base 9), A011540 (base 10).

Cf. A007094, A043421, A255805 (complement).

Select[Range[0, 300], DigitCount[#, 8, 0] > 0 &]

A004682 Primes written in base 8.

Original entry on oeis.org

2, 3, 5, 7, 13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 103, 107, 111, 117, 123, 131, 141, 145, 147, 153, 155, 161, 177, 203, 211, 213, 225, 227, 235, 243, 247, 255, 263, 265, 277, 301, 305, 307, 323, 337, 343, 345, 351, 357, 361, 373, 401, 407, 415, 417

Offset: 1

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. similar sequences listed in A004680.

Cf. A007094.

[Seqint(Intseq(NthPrime(n),8)): n in [1..60]]; // G. C. Greubel, Oct 10 2018

FromDigits/@IntegerDigits[Prime[Range[50]], 8] (* Vincenzo Librandi, Sep 03 2016 *)

a(n)=subst(Pol(digits(prime(n),8)),'x,10) \\ Charles R Greathouse IV, Nov 06 2013

vector(60, n, fromdigits(digits(prime(n), 8))) \\ G. C. Greubel, Oct 10 2018

a(n) = A007094(prime(n)). - Michel Marcus, Sep 03 2016

A037402 Numbers k such that every base-7 digit of k is a base-8 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40, 48, 57, 85, 94, 106, 114, 133, 142, 163, 171, 196, 204, 212, 220, 224, 225, 226, 227, 228, 229, 230, 236, 244, 277, 285, 305, 334, 342, 385, 392, 401, 540, 546, 547, 550, 597, 620, 629, 646, 688

Offset: 1

Clark Kimberling

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

Cf. A007093, A007094.

Cf. A037403, A037404.

import Data.List ((\\), nub)
a037402 n = a037402_list !! (n-1)
a037402_list = filter f [1..] where
   f x = null $ nub (ds 7 x) \\ nub (ds 8 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

b7b8Q[n_]:=Module[{idn7=Union[IntegerDigits[n,7]]},Intersection[ idn7, Union[ IntegerDigits[n,8]]]==idn7]; Select[Range[700],b7b8Q] (* Harvey P. Dale, Dec 15 2013 *)

A043282 Maximal run length in base 8 representation of n.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling

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

Cf. A007094 (base 8).

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

A043282[n_]:=Max[Map[Length,Split[IntegerDigits[n,8]]]];Array[A043282,100] (* Paolo Xausa, Sep 27 2023 *)

A043282(n, b=8)={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

from itertools import groupby
def A043282(n): return max(len(list(g)) for k, g in groupby(oct(n)[2:])) # Chai Wah Wu, Mar 09 2023

A083902 Number of divisors of n with the largest digit of the divisor <= 7 (base 10).

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 3, 2, 4, 2, 6, 2, 4, 4, 4, 2, 4, 1, 6, 4, 4, 2, 7, 3, 4, 3, 5, 1, 8, 2, 5, 4, 4, 4, 7, 2, 2, 3, 7, 2, 8, 2, 6, 5, 4, 2, 8, 2, 6, 4, 6, 2, 6, 4, 6, 3, 2, 1, 12, 2, 4, 5, 6, 4, 8, 2, 5, 3, 8, 2, 9, 2, 4, 6, 4, 4, 6, 1, 8, 3, 3, 1, 10, 3, 3, 2, 6, 1, 9, 3, 5, 3, 3, 2, 9, 1, 4, 4, 9, 2, 8, 2, 7, 8

Offset: 1

Reinhard Zumkeller, May 08 2003

Cf. A054055, A000005, A007094, A083894, A083895, A083901, A083903.

Table[Count[Divisors[n],?(Max[IntegerDigits[#]]<8&)],{n,110}] (* _Harvey P. Dale, Nov 01 2022 *)

a(n) = A083901(n) + A083894(n) = A083903(n) - A083895(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A007094(k) = 11.2915816168324913817... . - Amiram Eldar, Jan 04 2024

Definition clarified by Harvey P. Dale, Nov 01 2022

cp's OEIS Frontend

A037399 Numbers k such that every base-6 digit of k is a base-8 digit of k.

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A136381 Sequence A136380 shown in octal base.

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A136383 Sequence A136382 shown in octal base.

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A136385 Sequence A136384 shown in octal base.

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A217009 Multiples of 7 in base 8.

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A382417 Numbers with at least one zero in their base-8 representation.

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Mathematica

A004682 Primes written in base 8.

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Magma

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PARI

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A037402 Numbers k such that every base-7 digit of k is a base-8 digit of k.

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Haskell

Mathematica

A043282 Maximal run length in base 8 representation of n.

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Author

Keywords

Links

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Programs

Mathematica

PARI