A050622 -id:A050622 - cp's OEIS frontend

A050625 Divisible by 3^k (where k is digit length of a(n)).

3, 6, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, 540, 567, 594, 621, 648, 675, 702, 729, 756, 783, 810, 837, 864, 891, 918, 945, 972, 999, 1053, 1134, 1215, 1296, 1377, 1458

Offset: 1

Patrick De Geest, Jun 15 1999

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A035014, A050622, A050623.

Flatten[Table[3^n*Range[Ceiling[10^(n-1)/3^n],Floor[(10^n-1)/3^n]],{n,4}]] (* Harvey P. Dale, Feb 26 2015 *)
Select[Range[1500],Mod[#,3^IntegerLength[#]]==0&] (* Harvey P. Dale, Apr 04 2020 *)

A053313 a(n) contains n digits (either '2' or '9') and is divisible by 2^n.

Original entry on oeis.org

2, 92, 992, 2992, 92992, 292992, 2292992, 22292992, 222292992, 2222292992, 22222292992, 922222292992, 9922222292992, 29922222292992, 929922222292992, 9929922222292992, 99929922222292992, 999929922222292992

Offset: 1

Henry Bottomley, Mar 06 2000

Ray Chandler, Table of n, a(n) for n = 1..1000

Cf. A023400, A050621, A050622, A035014.

Select[Flatten[Table[FromDigits/@Tuples[{2,9},n],{n,18}]],Divisible[ #,2^IntegerLength[ #]]&] (* Harvey P. Dale, Feb 07 2015 *)

a(n)=a(n-1)+10^(n-1)*(2+7*[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 2, if not then n-th term begins with a 7.

A053314 a(n) contains n digits (either '1' or '4') and is divisible by 2^n.

Original entry on oeis.org

4, 44, 144, 4144, 14144, 414144, 1414144, 41414144, 441414144, 1441414144, 11441414144, 411441414144, 4411441414144, 44411441414144, 444411441414144, 1444411441414144, 41444411441414144, 441444411441414144

Offset: 1

Henry Bottomley, Mar 06 2000

Robert Israel, Table of n, a(n) for n = 1..999

Cf. A023401, A050621, A050622, A035014.

A[1]:= 4:
for n from 2 to 100 do
   if A[n-1] mod 2^n = 0 then A[n]:= A[n-1]+4*10^(n-1)
   else A[n]:= A[n-1]+10^(n-1)
fi
od:
seq(A[i],i=1..100); # Robert Israel, Oct 27 2019

nxt[{n_,a_}]:={n+1,If[Divisible[a,2^(n+1)],4*10^IntegerLength[a]+ a, 10^IntegerLength[ a]+a]}; NestList[nxt,{1,4},20][[All,2]] (* Harvey P. Dale, Oct 30 2022 *)

a(n) = a(n-1) + 10^(n-1)*(4 - 3*(a(n-1)/2^(n-1) mod 2)), i.e., a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 4, if not then n-th term begins with a 1.

Formula corrected by Robert Israel, Oct 27 2019

A053315 a(n) contains n digits (either '4' or '5') and is divisible by 2^n.

Original entry on oeis.org

4, 44, 544, 4544, 44544, 444544, 4444544, 54444544, 454444544, 5454444544, 45454444544, 545454444544, 5545454444544, 55545454444544, 555545454444544, 4555545454444544, 44555545454444544, 544555545454444544

Offset: 1

Henry Bottomley, Mar 06 2000

Robert Israel, Table of n, a(n) for n = 1..999

Cf. A023403, A050621, A050622, A035014.

A[1]:= 4:
for n from 2 to 100 do
   if A[n-1] mod 2^n = 0 then A[n]:= A[n-1]+4*10^(n-1)
   else A[n]:= A[n-1]+5*10^(n-1)
fi
od:
seq(A[i],i=1..100); # Robert Israel, Oct 27 2019

a(n) = a(n-1) + 10^(n-1)*(4 + (a(n-1)/2^(n-1) mod 2)), i.e., a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 4, if not then n-th term begins with a 5.

Formula corrected by Robert Israel, Oct 27 2019

A053333 a(n) contains n digits (either '4' or '9') and is divisible by 2^n.

Original entry on oeis.org

4, 44, 944, 4944, 94944, 994944, 4994944, 94994944, 494994944, 9494994944, 49494994944, 449494994944, 9449494994944, 99449494994944, 499449494994944, 9499449494994944, 49499449494994944, 949499449494994944

Offset: 1

Henry Bottomley, Mar 06 2000

Ray Chandler, Table of n, a(n) for n = 1..1000

Cf. A023405, A050621, A050622, A035014.

nxt[{n_,a_}]:=Module[{fd=If[Mod[a,2^(n+1)]==0,4,9]},{n+1,fd 10^IntegerLength[a]+a}]; NestList[ nxt,{1,4},20][[;;,2]] (* Harvey P. Dale, Jul 14 2023 *)

a(n)=a(n-1)+10^(n-1)*(4+5*[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 4, if not then n-th term begins with a 9.

A053334 a(n) contains n digits (either '1' or '6') and is divisible by 2^n.

Original entry on oeis.org

6, 16, 616, 1616, 11616, 111616, 6111616, 16111616, 616111616, 1616111616, 61616111616, 661616111616, 1661616111616, 61661616111616, 661661616111616, 6661661616111616, 66661661616111616, 666661661616111616

Offset: 1

Henry Bottomley, Mar 06 2000

Ray Chandler, Table of n, a(n) for n = 1..1000

Cf. A023406, A050621, A050622, A035014.

nxt[{n_,a_}]:={n+1,a+10^n (6-5*Mod[a/2^n,2])}; NestList[nxt,{1,6},20][[;;,2]] (* Harvey P. Dale, Aug 20 2025 *)

a(n)=a(n-1)+10^(n-1)*(6-5*[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 6, if not then n-th term begins with a 1.

A053335 a(n) contains n digits (either '3' or '6') and is divisible by 2^n.

Original entry on oeis.org

6, 36, 336, 6336, 66336, 366336, 6366336, 36366336, 636366336, 3636366336, 33636366336, 333636366336, 3333636366336, 33333636366336, 633333636366336, 3633333636366336, 33633333636366336, 333633333636366336

Offset: 1

Henry Bottomley, Mar 06 2000

Ray Chandler, Table of n, a(n) for n = 1..1000

Cf. A023407, A050621, A050622, A035014.

a(n)=a(n-1)+10^(n-1)*(6-3*[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 6, if not then n-th term begins with a 3.

A053336 a(n) contains n digits (either '5' or '6') and is divisible by 2^n.

Original entry on oeis.org

6, 56, 656, 6656, 66656, 566656, 6566656, 66566656, 666566656, 6666566656, 56666566656, 656666566656, 6656666566656, 66656666566656, 566656666566656, 6566656666566656, 56566656666566656, 556566656666566656

Offset: 1

Henry Bottomley, Mar 06 2000

Ray Chandler, Table of n, a(n) for n = 1..1000

Cf. A023408, A050621, A050622, A035014.

Block[{a = {6}, k, m, w}, Do[k = 1; If[Mod[a[[-1]], 2^i] == 0, Set[w, Prepend[ConstantArray[5, i - 1], 6]], Set[w, ConstantArray[5, i]]]; While[Mod[Set[m, FromDigits[w + PadLeft[IntegerDigits[k, 2], i]]], 2^i] != 0, k++]; AppendTo[a, m], {i, 2, 18}]; a] (* Michael De Vlieger, Dec 10 2020 *)

a(n) = a(n-1)+10^(n-1)*(6-[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 6, if not then n-th term begins with a 5.

Conjecture: a(n) = 10^n - A035014(n). - J. Lowell, Nov 16 2020

A053337 a(n) contains n digits (either '6' or '7') and is divisible by 2^n.

Original entry on oeis.org

6, 76, 776, 7776, 67776, 667776, 6667776, 66667776, 766667776, 6766667776, 66766667776, 666766667776, 7666766667776, 77666766667776, 777666766667776, 7777666766667776, 77777666766667776, 777777666766667776

Offset: 1

Henry Bottomley, Mar 06 2000

Ray Chandler, Table of n, a(n) for n = 1..1000

Cf. A023409, A050621, A050622, A035014.

Table[Select[FromDigits/@Tuples[{6,7},n],Divisible[#,2^IntegerLength[ #]]&], {n,18}]//Flatten (* Harvey P. Dale, Jul 10 2016 *)

a(n)=a(n-1)+10^(n-1)*(6+[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 6, if not then n-th term begins with a 7.

A053377 a(n) contains n digits (either '3' or '8') and is divisible by 2^n.

Original entry on oeis.org

8, 88, 888, 3888, 33888, 333888, 3333888, 83333888, 383333888, 3383333888, 33383333888, 833383333888, 8833383333888, 88833383333888, 888833383333888, 8888833383333888, 88888833383333888, 888888833383333888

Offset: 1

Henry Bottomley, Mar 06 2000

Ray Chandler, Table of n, a(n) for n = 1..1000

Cf. A023412, A050621, A050622, A035014.

Flatten[Table[Select[FromDigits/@Tuples[{3,8},n],Divisible[#,2^n]&],{n,18}]] (* Harvey P. Dale, Dec 25 2015 *)

a(n)=a(n-1)+10^(n-1)*(8-5*[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with an 8, if not then n-th term begins with a 3.

cp's OEIS Frontend

A050625 Divisible by 3^k (where k is digit length of a(n)).

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A053313 a(n) contains n digits (either '2' or '9') and is divisible by 2^n.

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A053314 a(n) contains n digits (either '1' or '4') and is divisible by 2^n.

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A053315 a(n) contains n digits (either '4' or '5') and is divisible by 2^n.

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A053333 a(n) contains n digits (either '4' or '9') and is divisible by 2^n.

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A053334 a(n) contains n digits (either '1' or '6') and is divisible by 2^n.

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A053335 a(n) contains n digits (either '3' or '6') and is divisible by 2^n.

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A053336 a(n) contains n digits (either '5' or '6') and is divisible by 2^n.

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A053337 a(n) contains n digits (either '6' or '7') and is divisible by 2^n.

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