A035014 -id:A035014 - cp's OEIS frontend

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

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.

A053378 a(n) contains n digits (either '5' or '8') and is divisible by 2^n.

Original entry on oeis.org

8, 88, 888, 5888, 85888, 885888, 8885888, 58885888, 558885888, 8558885888, 58558885888, 858558885888, 5858558885888, 85858558885888, 585858558885888, 5585858558885888, 55585858558885888, 855585858558885888

Offset: 1

Henry Bottomley, Mar 06 2000

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

Cf. A023413, A050621, A050622, A035014.

a(n)=a(n-1)+10^(n-1)*(8-3*[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 an 8, if not then n-th term begins with a 5.

A053379 a(n) contains n digits (either '7' or '8') and is divisible by 2^n.

Original entry on oeis.org

8, 88, 888, 7888, 77888, 877888, 7877888, 87877888, 787877888, 8787877888, 88787877888, 888787877888, 8888787877888, 88888787877888, 788888787877888, 8788888787877888, 88788888787877888, 888788888787877888

Offset: 1

Henry Bottomley, Mar 06 2000

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

Cf. A023414, 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 7.

A241882 Numbers with d digits that are divisible by 2^d and have at most 2 distinct digits: exactly one even digit and at most one odd digit.

Original entry on oeis.org

2, 4, 6, 8, 12, 16, 32, 36, 44, 52, 56, 72, 76, 88, 92, 96, 112, 144, 232, 272, 336, 344, 544, 552, 616, 656, 696, 744, 776, 888, 944, 992, 1616, 1888, 2112, 2272, 2992, 3232, 3344, 3888, 4144, 4544, 4944, 5552, 5888, 6336, 6656, 7744, 7776, 7888, 9696, 9888

Offset: 1

J. Lowell, Apr 30 2014

Union of 20 different sequences, all of which are defined as "a(n) contains n digits (either [any odd digit] or [any nonzero even digit] and is divisible by 2^n)."

Subsequence of A050622. - Michel Marcus, May 07 2014

			24 is not in the sequence because it has distinct even digits.

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A035014, A053312-A053318, A053332-A053338, A053376-A053380 (sequences whose union is this sequence).

isok(n) = {digs = digits(n); d = #digs; if (n % 2^d, return (0)); sd = Set(digs); if (#sd > 2, return (0)); if (#sd < 2, return (1)); ((sd[1] % 2) + (sd[2] % 2)) == 1;} \\ Michel Marcus, May 02 2014

More terms from Michel Marcus, May 02 2014

A284924 a(n) is the least n-digit multiple of 5^n using the decimal digits {5, 6, 7, 8, 9} exclusively.

Original entry on oeis.org

5, 75, 875, 6875, 96875, 796875, 6796875, 66796875, 966796875, 5966796875, 65966796875, 865966796875, 8865966796875, 68865966796875, 868865966796875, 8868865966796875, 78868865966796875, 578868865966796875, 7578868865966796875, 87578868865966796875

Offset: 1

J. Lowell, Apr 05 2017

			a(2) = 75 because 75 is divisible by 5^2 (25*3=75) and uses only digits in the 5-9 interval.

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Cf. A140288, A035014, A053312.

More terms from Alois P. Heinz, Apr 06 2017

cp's OEIS Frontend

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

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A053378 a(n) contains n digits (either '5' or '8') and is divisible by 2^n.

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A053379 a(n) contains n digits (either '7' or '8') and is divisible by 2^n.

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A241882 Numbers with d digits that are divisible by 2^d and have at most 2 distinct digits: exactly one even digit and at most one odd digit.

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A284924 a(n) is the least n-digit multiple of 5^n using the decimal digits {5, 6, 7, 8, 9} exclusively.

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