A050621 -id:A050621 - cp's OEIS frontend

A053338 a(n) contains n digits (either '6' or '9') and is divisible by 2^n.

6, 96, 696, 9696, 69696, 669696, 6669696, 96669696, 696669696, 9696669696, 69696669696, 969696669696, 9969696669696, 69969696669696, 969969696669696, 9969969696669696, 99969969696669696, 999969969696669696

Offset: 1

Henry Bottomley, Mar 06 2000

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

Cf. A023410, A050621, A050622, A035014.

Table[Select[FromDigits/@Tuples[{6,9},n],Mod[#,2^n]==0&],{n,20}]//Flatten (* Harvey P. Dale, Sep 15 2023 *)

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 9.

A053376 a(n) contains n digits (either '1' or '8') and is divisible by 2^n.

Original entry on oeis.org

8, 88, 888, 1888, 81888, 181888, 8181888, 18181888, 118181888, 8118181888, 88118181888, 888118181888, 8888118181888, 88888118181888, 888888118181888, 1888888118181888, 81888888118181888, 181888888118181888

Offset: 1

Henry Bottomley, Mar 06 2000

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

Cf. A023411, A050621, A050622, A035014.

Table[Select[FromDigits/@Tuples[{1,8},n],Divisible[#,2^n]&],{n,20}]// Flatten (* Harvey P. Dale, Aug 20 2017 *)

a(n)=a(n-1)+10^(n-1)*(8-7*[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 an 8, if not then n-th term begins with a 1.

A053380 a(n) contains n digits (either '8' or '9') and is divisible by 2^n.

Original entry on oeis.org

8, 88, 888, 9888, 89888, 989888, 9989888, 89989888, 989989888, 8989989888, 98989989888, 898989989888, 8898989989888, 98898989989888, 998898989989888, 8998898989989888, 98998898989989888, 898998898989989888

Offset: 1

Henry Bottomley, Mar 06 2000

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

Cf. A023415, A050621, A050622, A035014.

a(n)=a(n-1)+10^(n-1)*(8+[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 9.

A045583 Numbers k that divide 10^k + 2^k.

Original entry on oeis.org

1, 2, 3, 4, 8, 9, 16, 21, 26, 27, 32, 63, 64, 81, 128, 136, 147, 189, 243, 256, 338, 441, 512, 567, 609, 729, 903, 1024, 1029, 1252, 1323, 1378, 1701, 1827, 2048, 2187, 2312, 2667, 2709, 3087, 3969, 4096, 4263, 4394, 4401, 5103, 5481, 6321, 6561, 7203, 8001

Offset: 1

David W. Wilson

nonn

Amiram Eldar, Table of n, a(n) for n = 1..1500

Cf. A050621.

Select[Range[8100],Divisible[10^#+2^#,#]&]  (* Harvey P. Dale, Apr 02 2011 *)
Select[Range[8001], Divisible[PowerMod[2, #, #] + PowerMod[10, #, #], #] &] (* Amiram Eldar, Oct 23 2021 *)

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.

cp's OEIS Frontend

A053338 a(n) contains n digits (either '6' or '9') and is divisible by 2^n.

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A053376 a(n) contains n digits (either '1' or '8') and is divisible by 2^n.

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A053380 a(n) contains n digits (either '8' or '9') and is divisible by 2^n.

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A045583 Numbers k that divide 10^k + 2^k.

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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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