A069534 -id:A069534 - cp's OEIS frontend

A069537 Multiples of 2 whose digit sum is 2.

2, 20, 110, 200, 1010, 1100, 2000, 10010, 10100, 11000, 20000, 100010, 100100, 101000, 110000, 200000, 1000010, 1000100, 1001000, 1010000, 1100000, 2000000, 10000010, 10000100, 10001000, 10010000, 10100000, 11000000, 20000000, 100000010, 100000100, 100001000

Offset: 1

Amarnath Murthy, Apr 01 2002

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A002024, A002260, A088404 (half).
Cf. A069521 to A069530, A069532, A069534, A069536.
Subsequence of A005349.
Row n=2 of A245062.

a(n) = my(r,s=sqrtint((n-1)<<1,&r), x=s+(r>s), y=if(r>s,r-s,r+s)>>1); 10^x + 10^y; \\ Kevin Ryde, Jul 17 2025

from itertools import product
def agen():
  digits = 1
  while True:
    for i in range(digits-2): yield int("1"+"0"*(digits-3-i)+"1"+"0"*i+"0")
    yield int("2"+"0"*(digits-1))
    digits += 1
g = agen()
print([next(g) for i in range(32)]) # Michael S. Branicky, Feb 20 2021

a(n) = 10^A002024(n-1) + 10^A002260(n-1) for n >= 2. - Kevin Ryde, Jul 17 2025

Corrected and extended by Ray Chandler, Sep 28 2003

A063997 Multiples of 4 whose digits add to 4.

Original entry on oeis.org

4, 40, 112, 220, 400, 1012, 1120, 1300, 2020, 2200, 3100, 4000, 10012, 10120, 10300, 11020, 11200, 12100, 13000, 20020, 20200, 21100, 22000, 30100, 31000, 40000, 100012, 100120, 100300, 101020, 101200, 102100, 103000, 110020, 110200, 111100

Offset: 1

Lisa O. Coulter (lcoulter(AT)stetson.edu), Sep 06 2001

			4 is an element of the sequence, since 4 is a multiple of 4 the sum of whose digits is 4; 220 is an element of the sequence, since 220 = 4*55 and 2 + 2+ 0 = 4.

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 218 terms from Harry J. Smith)

Cf. A069521 to A069530, A069532, A069533, A069534, A069535, A069536, A069537, A052217.

Row n=4 of A245062.

Select[4Range[120000],Total[IntegerDigits[#]]==4&] (* Harvey P. Dale, May 07 2011 *)

SumDE(x,y)= { local(s); s=0; while (x>9 && sHarry J. Smith, Sep 05 2009

More terms from Ray Chandler, Sep 28 2003

A062768 Multiples of 6 such that the sum of the digits is equal to 6.

Original entry on oeis.org

6, 24, 42, 60, 114, 132, 150, 204, 222, 240, 312, 330, 402, 420, 510, 600, 1014, 1032, 1050, 1104, 1122, 1140, 1212, 1230, 1302, 1320, 1410, 1500, 2004, 2022, 2040, 2112, 2130, 2202, 2220, 2310, 2400, 3012, 3030, 3102, 3120, 3210, 3300, 4002, 4020, 4110

Offset: 1

Lisa O Coulter (lisa_coulter(AT)my-deja.com), Jul 17 2001

Even numbers with sum of digits equal to 6 are Harshad numbers (A005349). - Davide Rotondo, Sep 04 2020

			60 is a member of the sequence since 60 / 6 = 10 and 6 + 0 = 6; 114 is also an element since 114 is divisible by 6 and 1 + 1+ 4 = 6.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A063416, A069521 to A069530, A069532, A069533, A069534, A069535, A069536, A069537, A052217, A063997, A069540.
Subsequence of A005349.
Row n=6 of A245062.

: var stk: stack; end; minarg := 0; maxarg := 900; n := 6; for k := minarg to maxarg do m := k*n; s := itoa(m); for j := 0 to length(s) - 1 do stack_push(stk,atoi(s[j..j])); end; if sum(stack2array(stk)) = n then write(m," "); end; end;.

Select[ Range[ 6, 4200, 6 ], Plus @@ IntegerDigits[ # ] == 6 & ]

More terms from Klaus Brockhaus, Jul 20 2001

A063416 Multiples of 7 whose sum of digits is equal to 7.

Original entry on oeis.org

7, 70, 133, 322, 511, 700, 1015, 1141, 1204, 1330, 2023, 2212, 2401, 3031, 3220, 4102, 5110, 7000, 10024, 10150, 10213, 10402, 11032, 11221, 11410, 12040, 12103, 13111, 13300, 15001, 20041, 20104, 20230, 21112, 21301, 22120, 23002, 24010

Offset: 1

Klaus Brockhaus, Jul 20 2001

Numbers are all 7 mod 63.

			133 = 19*7 and 1+3+3 = 7, so 133 is a term of this sequence.

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 700 terms from Harry J. Smith)

Cf. A069521 to A069530, A069532, A069533, A069534, A069535, A069536, A069537, A052217, A063997, A069540, A062768.

Row n=7 of A245062.

: var stk: stack; end; minarg := 0; maxarg := 5000; n := 7; for k := minarg to maxarg do m := k*n; s := itoa(m); for j := 0 to length(s) - 1 do stack_push(stk,atoi(s[j..j])); end; if sum(stack2array(stk)) = n then write(m," "); end; end;.

Select[Range[7, 25000, 7], Plus @@ IntegerDigits[ # ] == 7 &]

forstep(m=0, 70000, 7, if(vecsum(digits(m))==7, print1(m, ", "))) \\ Harry J. Smith, Aug 20 2009

A069540 Multiples of 5 with digit sum 5.

Original entry on oeis.org

5, 50, 140, 230, 320, 410, 500, 1040, 1130, 1220, 1310, 1400, 2030, 2120, 2210, 2300, 3020, 3110, 3200, 4010, 4100, 5000, 10040, 10130, 10220, 10310, 10400, 11030, 11120, 11210, 11300, 12020, 12110, 12200, 13010, 13100, 14000, 20030, 20120

Offset: 1

Amarnath Murthy, Apr 01 2002

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A069521 to A069530, A069532, A069533, A069534, A069535, A069536, A069537, A052217, A063997.

Row n=5 of A245062.

Select[5*Range[5000],Total[IntegerDigits[#]]==5&] (* Harvey P. Dale, Nov 08 2017 *)

Corrected and extended by Ray Chandler, Sep 28 2003

A069543 Multiples of 8 with digit sum 8.

Original entry on oeis.org

8, 80, 152, 224, 440, 512, 800, 1016, 1160, 1232, 1304, 1520, 2024, 2240, 2312, 2600, 3032, 3104, 3320, 4040, 4112, 4400, 5120, 6200, 8000, 10016, 10160, 10232, 10304, 10520, 11024, 11240, 11312, 11600, 12032, 12104, 12320, 13040, 13112, 13400

Offset: 1

Amarnath Murthy, Apr 01 2002

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A069521 to A069530, A069532, A069533, A069534, A069535, A069536, A069537, A052217, A063997, A069540, A062768, A063416.

Row n=8 of A245062.

More terms from Ray Chandler, Sep 28 2003

A069536 Smallest multiple of 8 with digit sum n.

Original entry on oeis.org

0, 1000, 200, 120, 40, 32, 24, 16, 8, 72, 64, 56, 48, 184, 176, 96, 88, 296, 288, 496, 488, 696, 688, 896, 888, 1888, 2888, 3888, 4888, 5888, 6888, 7888, 8888, 9888, 19888, 29888, 39888, 49888, 59888, 69888, 79888, 89888, 99888

Offset: 0

Amarnath Murthy, Apr 01 2002

a(25) onwards the pattern is evident.

Cf. A069521 to A069530, A069532, A069533, A069534, A069535.

a069536 n = a069536_list !! n
a069536_list = map (* 8) a077495_list
-- Reinhard Zumkeller, Dec 09 2011

a(n) = 8 * A077495(n).

Missing a(0) inserted by Franklin T. Adams-Watters, Nov 29 2011

A077495 a(n) = smallest k such that the digit sum of 8k is n.

Original entry on oeis.org

0, 125, 25, 15, 5, 4, 3, 2, 1, 9, 8, 7, 6, 23, 22, 12, 11, 37, 36, 62, 61, 87, 86, 112, 111, 236, 361, 486, 611, 736, 861, 986, 1111, 1236, 2486, 3736, 4986, 6236, 7486, 8736, 9986, 11236, 12486, 24986, 37486, 49986, 62486, 74986, 87486, 99986, 112486, 124986

Offset: 0

Amarnath Murthy, Nov 07 2002

A069536(n)/8.

Cf. A051885, A069532, A069534, A069536, A077493, A077494.

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a077495 n = fromJust $ elemIndex n $ map a007953 a008590_list
a077495_list = map a077495 [0..]
-- Reinhard Zumkeller, Dec 09 2011

From Robert Israel, Nov 19 2022: (Start) G.f.: -x^24*(985*x^9 - 125*x^8 - 125*x^7 - 125*x^6 - 125*x^5 - 125*x^4 - 125*x^3 - 125*x^2 - 125*x - 111)/((x - 1)*(10*x^9 - 1)) + 112*x^23 + 86*x^22 + 87*x^21 + 61*x^20 + 62*x^19 + 36*x^18 + 37*x^17 + 11*x^16 + 12*x^15 + 22*x^14 + 23*x^13 + 6*x^12 + 7*x^11 + 8*x^10 + 9*x^9 + x^8 + 2*x^7 + 3*x^6 + 4*x^5 + 5*x^4 + 15*x^3 + 25*x^2 + 125*x.

For n >= 24, a(n) = 125*A051885(n-24) + 111. (End)

Corrected and extended by Ray Chandler, Aug 03 2003

Missing a(0)=0 added and offset adjusted by Reinhard Zumkeller, Dec 09 2011

A077491 a(n) = smallest k such that 2k has digit sum = n.

Original entry on oeis.org

5, 1, 6, 2, 7, 3, 8, 4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 99, 149, 199, 249, 299, 349, 399, 449, 499, 999, 1499, 1999, 2499, 2999, 3499, 3999, 4499, 4999, 9999, 14999, 19999, 24999, 29999, 34999, 39999, 44999, 49999, 99999, 149999, 199999, 249999, 299999

Offset: 1

Amarnath Murthy, Nov 07 2002

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,10,-10).

Cf. A069532, A069534.

a(n) = A069532(n)/2.

More terms from Ray Chandler, Jul 28 2003

A077492 a(n) = smallest k such that 5k has a digit sum = n.

Original entry on oeis.org

2, 4, 6, 8, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 39, 59, 79, 99, 119, 139, 159, 179, 199, 399, 599, 799, 999, 1199, 1399, 1599, 1799, 1999, 3999, 5999, 7999, 9999, 11999, 13999, 15999, 17999, 19999, 39999, 59999, 79999, 99999, 119999, 139999, 159999, 179999

Offset: 1

Amarnath Murthy, Nov 07 2002

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,10,-10).

Cf. A069532, A069534.

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 10, -10},{2, 4, 6, 8, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19}, 40] (* Georg Fischer, Oct 26 2020 *)

a(n) = A069534(n)/5.

a(n) = a(n-1) + 10*a(n-9) - 10*a(n-10) for n > 14. - Georg Fischer, Oct 26 2020

More terms from Ray Chandler, Jul 28 2003

cp's OEIS Frontend

A069537 Multiples of 2 whose digit sum is 2.

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A063997 Multiples of 4 whose digits add to 4.

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A062768 Multiples of 6 such that the sum of the digits is equal to 6.

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A063416 Multiples of 7 whose sum of digits is equal to 7.

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A069540 Multiples of 5 with digit sum 5.

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A069543 Multiples of 8 with digit sum 8.

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A069536 Smallest multiple of 8 with digit sum n.

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A077495 a(n) = smallest k such that the digit sum of 8k is n.

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Haskell