A050621 -id:A050621 - cp's OEIS frontend

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

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.

A199045 Smallest multiple of 2^n having in decimal representation exactly n digits <= 2.

Original entry on oeis.org

2, 12, 112, 1120, 10112, 101120, 1002112, 10010112, 100101120, 1001011200, 10002010112, 100012122112, 1000121221120, 10001212211200, 100002002010112, 1000000210010112, 10000002100101120, 100000021001011200, 1000000210010112000, 10000000201221210112

Offset: 1

Reinhard Zumkeller, Nov 02 2011

A050621(n) <= a(n) < A050621(n+1); A054055(a(n)) <= 2.

			n=3: A050621(3) = 104 = 8 * 13, a(3) = 112 = 8 * 14;
n=4: A050621(4) = 1008 = 16 * 63, a(4) = 1120 = 16 * 70.

Reinhard Zumkeller, Table of n, a(n) for n = 1..32

Cf. A000079, A034478, A159952.

a199045 n = head $
   filter ((<= 2) . a054055) $ map (* 2^n) [a034478 (n-1)..]

cp's OEIS Frontend

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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A199045 Smallest multiple of 2^n having in decimal representation exactly n digits <= 2.

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