A007091 -id:A007091 - cp's OEIS frontend

A374736 a(n) is the least number of the form k*n for some k > 0 that can be added to n without carries in decimal.

0, 1, 2, 3, 4, 10, 12, 21, 40, 90, 10, 11, 12, 13, 14, 30, 32, 51, 180, 380, 20, 21, 22, 23, 24, 50, 52, 162, 140, 870, 30, 31, 32, 33, 34, 140, 252, 111, 760, 1560, 40, 41, 42, 43, 44, 450, 230, 141, 240, 2450, 100, 102, 104, 106, 324, 110, 112, 342, 1740

Offset: 0

Rémy Sigrist, Jul 18 2024

			For n = 8:
- 1*8 = 8; computing 8 + 8 requires a carry,
- 2*8 = 16; computing 8 + 16 requires a carry,
- 3*8 = 24; computing 8 + 24 requires a carry,
- 4*8 = 32; computing 8 + 32 requires a carry,
- 5*8 = 40; computing 8 + 40 does not require a carry,
- so a(8) = 40.

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Cf. A007091, A261892 (analog for binary), A353624 (analog for balanced ternary), A374735.

a(n, base = 10) = { for (k = 1, oo, if (sumdigits((k+1)*n, base) == sumdigits(n, base) + sumdigits(k*n, base), return (k*n); ); ); }

from itertools import count
def A374736(n):
    s = list(map(int,str(n)[::-1]))
    return next(k for k in count(n,n) if all(a+b<=9 for a, b in zip(s,map(int,str(k)[::-1])))) # Chai Wah Wu, Jul 19 2024

a(n) = A374735(n) * n.
a(n) = n iff n belongs to A007091.
a(10*n) = 10*a(n).

A001740 Squares written in base 5.

Original entry on oeis.org

0, 1, 4, 14, 31, 100, 121, 144, 224, 311, 400, 441, 1034, 1134, 1241, 1400, 2011, 2124, 2244, 2421, 3100, 3231, 3414, 4104, 4301, 10000, 10201, 10404, 11114, 11331, 12100, 12321, 13044, 13324, 14111, 14400, 20141, 20434, 21234, 22041, 22400, 23211, 24024

Offset: 0

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 0..1000

Table[FromDigits[IntegerDigits[n^2, 5]], {n, 0, 50}] (* T. D. Noe, Aug 10 2012 *)

a(n) = A007091(A000290(n)). - Jason Kimberley, Dec 13 2012

A004635 Cubes written in base 5.

Original entry on oeis.org

1, 13, 102, 224, 1000, 1331, 2333, 4022, 10404, 13000, 20311, 23403, 32242, 41434, 102000, 112341, 124123, 141312, 204414, 224000, 244021, 320043, 342132, 420244, 1000000, 1030301, 1112213, 1200302, 1240024, 1331000, 1423131, 2022033, 2122222, 2224204

Offset: 1

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A000578, A007091.

[Seqint(Intseq(n^3, 5)): n in [1..30]]; // Vincenzo Librandi, Oct 15 2015

Table[FromDigits[IntegerDigits[n^3, 5]], {n, 35}] (* Vincenzo Librandi, Oct 15 2015 *)

for(n=1,30, print1(fromdigits(digits(n^3, 5)), ", ")) \\ G. C. Greubel, Sep 10 2018

a(n) = A007091(n^3) = A007091(A000578(n)). - Michel Marcus, Oct 15 2015

Changed offset and more terms from Vincenzo Librandi, Oct 15 2015

A023061 Positive numbers k such that k and 2*k are anagrams in base 5 (written in base 5).

Original entry on oeis.org

13, 130, 143, 1300, 1313, 1430, 1443, 13000, 13013, 13130, 13143, 14300, 14313, 14430, 14443, 102342, 103242, 120234, 120324, 130000, 130013, 130130, 130143, 131300, 131313, 131430, 131443, 143000, 143013, 143130, 143143, 144300, 144313

Offset: 1

David W. Wilson

From Robert Israel, Aug 08 2018: (Start)
The concatenation of two terms is a term.
If a*10^m + b is a term, where b < (2/9)*10^m, then a*10^k+b is a term for all k > m. (End)

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Robert Israel)

Cf. A007091.

f:= proc(n) local L, M;
   L:= convert(n, base, 5);
   M:= convert(2*n, base, 5);
   if sort(L) = sort(M) then add(L[i]*10^(i-1), i=1..nops(L)) else NULL fi
end proc:
map(f, [$1..10000]); # Robert Israel, Aug 08 2018

FromDigits[IntegerDigits[#, 5]] & /@ Select[Range[10000], SameQ @@ Sort /@ IntegerDigits[{#, 2*#}, 5] &] (* Amiram Eldar, Aug 06 2025 *)

A023062 Positive numbers k such that k and 3*k are anagrams in base 5 (written in base 5).

Original entry on oeis.org

1032, 1234, 10032, 10320, 10322, 10432, 11402, 12014, 12234, 12340, 12344, 12434, 100032, 100320, 100322, 100432, 101343, 103200, 103220, 103222, 103321, 104320, 104322, 104432, 110332, 112334, 114002, 114020, 114022, 114402, 120014, 120140

Offset: 1

David W. Wilson

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007091.

FromDigits[IntegerDigits[#, 5]] & /@ Select[Range[10000], SameQ @@ Sort /@ IntegerDigits[{#, 3*#}, 5] &] (* Amiram Eldar, Aug 06 2025 *)

A023063 Positive numbers k such that k and 4*k are anagrams in base 5 (written in base 5).

Original entry on oeis.org

1034, 10034, 10340, 10344, 10434, 100034, 100340, 100344, 100434, 102243, 102342, 102423, 103400, 103440, 103444, 104340, 104344, 104434, 1000034, 1000340, 1000344, 1000434, 1002243, 1002342, 1002423, 1003400, 1003440, 1003444, 1004340

Offset: 1

David W. Wilson

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007091.

FromDigits[IntegerDigits[#, 5]] & /@ Select[Range[30000], SameQ @@ Sort /@ IntegerDigits[{#, 4*#}, 5] &] (* Amiram Eldar, Aug 06 2025 *)

A031473 Numbers whose base-5 representation has 3 more 0's than 4's.

Original entry on oeis.org

125, 250, 375, 626, 627, 628, 630, 635, 640, 650, 675, 700, 750, 875, 1000, 1251, 1252, 1253, 1255, 1260, 1265, 1275, 1300, 1325, 1375, 1500, 1625, 1876, 1877, 1878, 1880, 1885, 1890, 1900, 1925, 1950, 2000, 2125, 2250

Offset: 1

Clark Kimberling

Cf. A007091.

Select[Range[2300],DigitCount[#,5,0]==DigitCount[#,5,4]+3&] (* Harvey P. Dale, Jul 23 2012 *)

A031476 Numbers whose base-5 representation has 3 fewer 0's than 4's.

Original entry on oeis.org

124, 249, 374, 499, 549, 574, 599, 609, 614, 619, 621, 622, 623, 874, 999, 1124, 1174, 1199, 1224, 1234, 1239, 1244, 1246, 1247, 1248, 1499, 1624, 1749, 1799, 1824, 1849, 1859, 1864, 1869, 1871, 1872, 1873, 2124, 2249

Offset: 1

Clark Kimberling

Cf. A007091.

A031957 Numbers with exactly three distinct base-5 digits.

Original entry on oeis.org

27, 28, 29, 35, 38, 39, 40, 42, 44, 45, 47, 48, 51, 53, 54, 55, 58, 59, 65, 66, 69, 70, 71, 73, 76, 77, 79, 80, 82, 84, 85, 86, 89, 95, 96, 97, 101, 102, 103, 105, 107, 108, 110, 111, 113, 115, 116, 117, 127, 128, 129, 132, 133, 134

Offset: 1

Clark Kimberling

Cf. A007091.

A032940 Numbers whose base-5 representation Sum_{i=0..m} d(i)*5^(m-i) has d(i)=0 for all odd i.

Original entry on oeis.org

1, 2, 3, 4, 5, 10, 15, 20, 25, 26, 27, 28, 29, 50, 51, 52, 53, 54, 75, 76, 77, 78, 79, 100, 101, 102, 103, 104, 125, 130, 135, 140, 145, 250, 255, 260, 265, 270, 375, 380, 385, 390, 395, 500, 505, 510, 515, 520, 625, 626, 627, 628, 629

Offset: 1

Clark Kimberling

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

Cf. A007091 (numbers in base 5).

f:= proc(n,j) local L,m;
  L:= convert(n,base,5);
  m:= nops(L);
  j*add(L[i+1]*5^(2*i),i=0..m-1)
end proc:
seq(seq(seq(f(n,j),n=5^k..5^(k+1)-1),j=[1,5]),k=0..2); # Robert Israel, Nov 15 2020

Definition corrected by Robert Israel, Nov 15 2020

cp's OEIS Frontend

A374736 a(n) is the least number of the form k*n for some k > 0 that can be added to n without carries in decimal.

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A001740 Squares written in base 5.

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A004635 Cubes written in base 5.

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Magma

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A023061 Positive numbers k such that k and 2*k are anagrams in base 5 (written in base 5).

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Maple

Mathematica

A023062 Positive numbers k such that k and 3*k are anagrams in base 5 (written in base 5).

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Mathematica

A023063 Positive numbers k such that k and 4*k are anagrams in base 5 (written in base 5).

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Mathematica

A031473 Numbers whose base-5 representation has 3 more 0's than 4's.

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Mathematica

A031476 Numbers whose base-5 representation has 3 fewer 0's than 4's.

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A031957 Numbers with exactly three distinct base-5 digits.

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A032940 Numbers whose base-5 representation Sum_{i=0..m} d(i)*5^(m-i) has d(i)=0 for all odd i.

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