A032532 -id:A032532 - cp's OEIS frontend

A032533 Numbers that, when expressed in base 2 and then interpreted in base 10, yield a multiple of the original number.

1, 2, 4, 8, 10, 16, 20, 21, 32, 40, 42, 64, 80, 84, 100, 128, 160, 168, 200, 256, 273, 320, 336, 400, 512, 546, 640, 672, 800, 1000, 1024, 1092, 1280, 1344, 1600, 2000, 2048, 2184, 2231, 2510, 2560, 2688, 2730, 3200, 3300, 4000, 4096, 4368, 4462

Offset: 1

Patrick De Geest, Apr 15 1998

nonn

Note that A025612 is a subset of this sequence (numbers of form 2^i*10^j, with i, j >= 0).

			8 in base 2 is 1000, which interpreted in base 10 is 1000 = 125*8.

Giovanni Resta, Table of n, a(n) for n = 1..1212 (terms < 3*10^11, first 251 terms from Paolo P. Lava)

Cf. A032532, A032534, A007088.

[k:k in [1..5000]| Seqint(Intseq(k,2)) mod k eq 0]; // Marius A. Burtea, Oct 11 2019

Select[Range[10000], Mod[FromDigits[IntegerDigits[#, 2]], #] == 0 &] (* Carl Najafi, Aug 18 2011 *)

select( is_A032533(n)=fromdigits(binary(n))%n==0, [1..5000]) \\ M. F. Hasler, Oct 11 2019

A032533 = { m : m divides A007088(m) }. - M. F. Hasler, Oct 11 2019

Example and better description from Erich Friedman, Jul 21 2001
Edited by Erich Friedman, Feb 09 2002
Offset set to 1 by Giovanni Resta, Jul 13 2016
Name edited by Jon E. Schoenfield, Oct 25 2019

A032549 Numbers that, when expressed in base 7 and then interpreted in base 10, yield a multiple of the original number.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 51, 102, 105, 153, 156, 207, 210, 258, 261, 312, 315, 2589, 2590, 2601, 2753, 5354, 5355, 5506, 8108, 8259, 8260, 10861, 11013, 11025, 13614, 13615, 13626, 13766, 13778, 16379, 16380, 16531, 33045, 140403, 289065, 1123224

Offset: 1

Patrick De Geest, Apr 15 1998

Decimal 'base-7 looking' numbers divided by their actual base-7 values (n) is an integer.

Giovanni Resta, Table of n, a(n) for n = 1..70 (terms < 10^12, first 63 terms from Paolo P. Lava)

Cf. A032548, A032550. See also A032532 for explanation.

Select[Range@ 300000, Mod[ FromDigits[ IntegerDigits[#, 7]], #] == 0 &] (* Giovanni Resta, Oct 21 2019 *)

Offset set to 1 by Giovanni Resta, Oct 21 2019

Name edited by Jon E. Schoenfield, Oct 25 2019

A032540 Numbers that, when expressed in base 4 and then interpreted in base 10, yield a multiple of the original number.

Original entry on oeis.org

0, 1, 2, 3, 6, 24, 120, 171, 177, 273, 362, 440, 546, 819, 1418, 1560, 1582, 1638, 1760, 1806, 2400, 2841, 2927, 3640, 4706, 4882, 5720, 6328, 6552, 7040, 7224, 9431, 9600, 10101, 14560, 20202, 22880, 24800, 25080, 25312, 28896, 32760, 36974, 38400

Offset: 1

Patrick De Geest, Apr 15 1998

n such that A007090(n) is a multiple of n. - Robert Israel, Sep 13 2018

			24 in base 4 is 120, which interpreted in base 10 is 120 = 5*24.

Giovanni Resta, Table of n, a(n) for n = 1..153 (terms < 5*10^12, first 100 terms from Robert Israel)

Cf. A032539, A032541, A032532.

filter:= proc(n) local L,t;
  L:= convert(n,base,4);
  t:= add(L[i]*10^(i-1),i=1..nops(L));
  t mod n = 0
end proc:
filter(0):=true:
select(filter, [$0..10^5]); # Robert Israel, Sep 13 2018

Join[{0}, Select[Range[40000], Divisible[FromDigits[IntegerDigits[#,4]], #]&]]  (* Harvey P. Dale, Apr 20 2011 *)

More terms from Erich Friedman and Naohiro Nomoto, Aug 06 2001
Offset changed by Robert Israel, Sep 13 2018
Name edited by Jon E. Schoenfield, Oct 25 2019

A032551 Numbers that, when expressed in base 8 and then interpreted in base 10, yield a multiple of the original number.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 34217, 34354, 68582, 68719, 68720, 70525, 70537, 70674, 104891, 104902, 105039, 105040, 106845, 139257, 141211, 141348, 175577, 175714, 177519, 177520, 177668, 211885, 212022, 212034, 213839, 213840, 248205, 248342, 250148

Offset: 1

Patrick De Geest, Apr 15 1998

Decimal 'base-8 looking' numbers divided by their actual base-8 value is an integer.

There are only 37 terms up to 30 million. - Harvey P. Dale, Sep 29 2012

			7 in base 8 is 7, which interpreted in base 10 is 7=1*7.

Giovanni Resta, Table of n, a(n) for n = 1..52 (first 37 terms from Harvey P. Dale)

Cf. A032552. See also A032532.

Join[{0},Select[Range[300000],Divisible[FromDigits[ IntegerDigits[ #,8]],#]&]] (* Harvey P. Dale, Sep 29 2012 *)

Edited by N. J. A. Sloane, Jun 07 2008 at the suggestion of Sergio Pimentel

Name edited by Jon E. Schoenfield, Oct 25 2019

A032538 Quotient of 'base-3' division described in A032537.

Original entry on oeis.org

1, 1, 3, 8, 8, 10, 29, 111, 85, 111, 104, 101, 370, 286, 286, 370, 333, 1105, 888, 1312, 1219, 1110, 1115, 3737, 3634, 3303, 2960, 3700, 14853, 14232, 11010, 49510, 47440, 44444, 36700, 45211, 42815, 147741, 112398, 108115, 154789, 492470

Offset: 1

Patrick De Geest, Apr 15 1998

nonn

Giovanni Resta, Table of n, a(n) for n = 1..135

Cf. A032536, A032537. See also A032532 for explanation.

Select[ FromDigits@ IntegerDigits[#, 3] / # & /@ Range[10^5], IntegerQ] (* Giovanni Resta, Jul 13 2016 *)

Offset set to 1 by Giovanni Resta, Jul 13 2016

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.

A032546 Numbers that, when expressed in base 6 and then interpreted in base 10, yield a multiple of the original number.

Original entry on oeis.org

1, 2, 3, 4, 5, 308, 4920, 11284, 11914, 144393, 195453, 518659, 866358, 925148, 1010765, 1172718, 1369865, 2141968, 2557924, 4287428, 4296908, 6064590, 8219190, 15347544, 16891738, 18409156, 18532263, 21880744, 23693054

Offset: 1

Patrick De Geest, Apr 15 1998

Original name: Decimal 'base 6 looking' numbers divided by their actual base 6 values (n) is an integer.

			308 is a term: 308_10 = 1232_6; 1232 = 308*4. - _Jon E. Schoenfield_, Oct 25 2019

Cf. A032545, A032547. See also A032532 for explanation.

Offset changed and Name edited by Jon E. Schoenfield, Oct 25 2019

A032548 Integer part of decimal 'base-7 looking' numbers divided by their actual base-7 values.

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

Offset: 1

Patrick De Geest, Apr 15 1998

Antti Karttunen, Table of n, a(n) for n = 1..35000

Cf. A007093, A032549, A032550. See also A032532 for explanation.

Array[IntegerPart[FromDigits[#]/FromDigits[#, 7]] &@ IntegerDigits[#, 7] &, 100] (* Michael De Vlieger, Jan 03 2019 *)

A007093(n) = if(n<=1,n,(10*A007093(n\7))+(n%7));
A032548(n) = (A007093(n)\n); \\ Antti Karttunen, Jan 01 2019

a(n) = floor(A007093(n)/n). - Antti Karttunen, Jan 01 2019

Offset corrected by Antti Karttunen, Jan 01 2019

A032534 Quotient of 'base-2' division described in A032533.

Original entry on oeis.org

1, 5, 25, 125, 101, 625, 505, 481, 3125, 2525, 2405, 15625, 12625, 12025, 11001, 78125, 63125, 60125, 55005, 390625, 366337, 315625, 300625, 275025, 1953125, 1831685, 1578125, 1503125, 1375125, 1111101, 9765625, 9158425, 7890625

Offset: 1

Patrick De Geest, Apr 15 1998

nonn

Cf. A032532, A032533.

Array[If[Mod[#2, #1] == 0, #2/#1, Nothing] & @@ {#, FromDigits[IntegerDigits[#, 2]]} &, 10^3] (* Michael De Vlieger, Oct 06 2019 *)

Offset 1 from Michael De Vlieger, Oct 06 2019

A032536 Integer part of decimal 'base-3 looking' numbers divided by their actual base-3 values.

Original entry on oeis.org

1, 1, 3, 2, 2, 3, 3, 2, 11, 10, 9, 9, 8, 8, 8, 7, 7, 11, 10, 10, 10, 9, 9, 9, 8, 8, 37, 35, 34, 33, 32, 31, 30, 30, 29, 30, 29, 29, 28, 27, 27, 26, 26, 25, 26, 26, 25, 25, 24, 24, 23, 23, 23, 37, 36, 35, 35, 34, 34, 33, 33, 32, 33, 32, 32, 31, 31, 31, 30, 30, 29, 30, 30

Offset: 1

Patrick De Geest, Apr 15 1998

Cf. A007089, A032537, A032538. See also A032532 for explanation.

Quotient[ FromDigits /@ IntegerDigits[ Range@ 73, 3], Range@ 73] (* Giovanni Resta, Jul 12 2016 *)

a(n) = floor(A007089(n)/n).

Offset corrected by Giovanni Resta, Jul 12 2016

cp's OEIS Frontend

A032533 Numbers that, when expressed in base 2 and then interpreted in base 10, yield a multiple of the original number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions

A032549 Numbers that, when expressed in base 7 and then interpreted in base 10, yield a multiple of the original number.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A032540 Numbers that, when expressed in base 4 and then interpreted in base 10, yield a multiple of the original number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A032551 Numbers that, when expressed in base 8 and then interpreted in base 10, yield a multiple of the original number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A032538 Quotient of 'base-3' division described in A032537.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A032546 Numbers that, when expressed in base 6 and then interpreted in base 10, yield a multiple of the original number.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A032548 Integer part of decimal 'base-7 looking' numbers divided by their actual base-7 values.

Views

Author

Keywords

Links