Matthew Cook - cp's OEIS frontend

A031142 Position of rightmost 0 (including leading 0) in 2^n increases.

0, 4, 7, 13, 14, 18, 24, 27, 31, 34, 37, 49, 51, 67, 72, 76, 77, 81, 86, 129, 176, 229, 700, 1757, 1958, 7931, 57356, 269518, 411658, 675531, 749254, 4400728, 18894561, 33250486, 58903708, 297751737, 325226398, 781717865, 18504580518, 27893737353

Offset: 1

Matthew Cook, Dan Hoey, Eric W. Weisstein, David W. Wilson

"Positions" are counted 0,1,2,3,... starting with the least significant digit.

86 is the last n for which the rightmost zero is the leading zero.

Alan Griffiths, Table of n, a(n) for n = 1..46 (reuploaded from a-file by _Georg Fischer_, Jan 21 2019)

Cf. A031140, A031141, A031142, A031143.

best = 0;
Select[Range[0, 10000],
 If[(t = First@
       First@StringPosition[StringReverse@("0" <> ToString@(2^#)),
"0"]) > best, best = t; True] &] (* Robert Price, Oct 11 2019 *)

a(39)-a(41) added (to match A031140) by Tanya Khovanova, Feb 02 2011

a(42)-a(44) from Alan Griffiths, Jan 25 2012

A031143 Position of rightmost 0 (including leading 0) in 2^A031142(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 21, 22, 23, 24, 25, 26, 36, 38, 54, 57, 59, 93, 115, 119, 120, 121, 136, 138, 164, 174, 176, 191, 196, 212, 217, 227, 233, 249, 250, 260, 268, 275, 308

Offset: 1

Matthew Cook, Dan Hoey, Eric W. Weisstein, David W. Wilson

nonn

"Positions" are counted 0,1,2,3,... starting with the least significant digit.

Cf. A031140, A031141, A031142, A031143.

best = 0; lst = {};
x = Select[Range[0, 10000],
  If[(t = First@
        First@StringPosition[StringReverse@("0" <> ToString@(2^#)),
          "0"]) > best, best = t; AppendTo[lst, t - 1]; True] &] ; lst (* Robert Price, Oct 11 2019 *)

More terms from Dan Hoey
a(42)-a(44) from Alan Griffiths, Jan 25 2012
a(45) from Alan Griffiths, Feb 01 2012
a(46) from Alan Griffiths, Mar 09 2012

A014582 Orders of magic squares whose rows and columns all have different sum-of-squares values (except for the necessary 180-degree symmetry).

Original entry on oeis.org

3, 23, 43, 47, 61, 67, 113, 127, 137, 149, 173, 193, 199

Offset: 1

Matthew Cook, Dec 11 1999

Index entries for sequences related to magic squares

A030222 Number of n-polyplets (polyominoes connected at edges or corners); may contain holes.

Original entry on oeis.org

1, 2, 5, 22, 94, 524, 3031, 18770, 118133, 758381, 4915652, 32149296, 211637205, 1401194463, 9321454604, 62272330564, 417546684096

Offset: 1

Matthew Cook

See A056840 for illustrations, valid also for this sequence up to n=4, but slightly misleading for polyplets with holes. See the colored areas in the illustration of A056840(5)=99 which correspond to identical 5-polyplets. (The 2+2+4-3 = 5 additional figures counted there correspond to the 4-square configuration with a hole inside ({2,4,6,8} on a numeric keyboard), with one additional square added in three inequivalent places: "inside" one angle (touching two sides), attached to one side, and attached to a corner. These do only count for 3 here, but for 8 in A056840.) It can be seen that A056840 counts a sort of "spanning trees" instead, i.e., simply connected graphs that connect all of the vertices (using only "King's moves", and maybe other additional constraints). - M. F. Hasler, Sep 29 2014

			XXX..XX...XX..X.X..X.. (the 5 for n=3)
.......X...X...X....X.
.....................X

M. F. Hasler, Illustration of A030222(5)=94 through a colored version of Vicher's image for A056840(5)=99. (Figures filled with same color do not count as different here.)
Eric Weisstein's World of Mathematics, Polyplet.
Wikipedia, Pseudo-polyomino

Cf. A006770.

10th row of A366766.

Computed by Matthew Cook; extended by David W. Wilson

More terms from Joseph Myers, Sep 26 2002

A031140 Position of rightmost 0 in 2^n increases.

Original entry on oeis.org

10, 20, 30, 40, 46, 68, 93, 95, 129, 176, 229, 700, 1757, 1958, 7931, 57356, 269518, 411658, 675531, 749254, 4400728, 18894561, 33250486, 58903708, 297751737, 325226398, 781717865, 18504580518, 27893737353, 103233492954

Offset: 1

Matthew Cook, Dan Hoey, Eric W. Weisstein, David W. Wilson

"Positions" are counted 0,1,2,3,... starting with the least significant digit.

I.e., look for increasing number of nonzero digits after the rightmost digit '0'. - M. F. Hasler, Jun 21 2018

			From _M. F. Hasler_, Jun 21 2018: (Start)
2^10 = 1024 is the first power of 2 to have a digit '0', which is the third digit from the right, i.e., it has to its right no digit '0' and two nonzero digits.
2^20 = 1048576 is the next larger power with a digit '0' having to its right no digit '0' and more (namely 5) nonzero digits than the above 1024.
After 2^46 = 70368744177664 there is 2^52 = 4503599627370496 having a '0' further to the left, but this digit has another '0' to its right and therefore cannot be considered: The next term having more nonzero digits after its rightmost '0' is only 2^68. (End)

Eric Weisstein's World of Mathematics, Zero.

Cf. A031141, A031142, A031143.

best = 0;
Select[Range[10000],
 If[(t = First@
       First@StringPosition[StringReverse@ToString@(2^#), "0"]) >
best, best = t; True] &] (* Robert Price, Oct 11 2019 *)

m=0;for(k=0,oo,d=digits(2^k);for(j=0,#d-1,d[#d-j]||(j>m&&(m=j)&&print1(k",")||break))) \\ M. F. Hasler, Jun 21 2018

More terms from Dan Hoey.

A031141 Position of rightmost digit 0 in 2^A031140(n).

Original entry on oeis.org

2, 5, 8, 11, 12, 13, 14, 23, 36, 38, 54, 57, 59, 93, 115, 119, 120, 121, 136, 138, 164, 174, 176, 191, 196, 212, 217, 227, 233, 249

Offset: 1

Matthew Cook, Dan Hoey, Eric W. Weisstein, David W. Wilson

"Positions" are counted 0,1,2,3,... starting with the least significant digit.

Eric Weisstein's World of Mathematics, Zero.

Cf. A031140, A031142, A031143.

best = 0;
x = Select[Range[10000],
  If[(t = First@
        First@StringPosition[StringReverse@ToString@(2^#), "0"]) >
     best, best = t; True] &] ;
First /@ First /@
   StringPosition[StringReverse[ToString /@ (2^x)],
"0"] - 1  (* Robert Price, Oct 11 2019 *)

m=0;for(k=0,oo,d=digits(2^k);for(j=0,#d-1,d[#d-j]||(j>m&&print1(m=j,",")||break))) \\ M. F. Hasler, Jun 21 2018

More terms from Dan Hoey

cp's OEIS Frontend

User: Matthew Cook

A031142 Position of rightmost 0 (including leading 0) in 2^n increases.

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A031143 Position of rightmost 0 (including leading 0) in 2^A031142(n).

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A014582 Orders of magic squares whose rows and columns all have different sum-of-squares values (except for the necessary 180-degree symmetry).

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A030222 Number of n-polyplets (polyominoes connected at edges or corners); may contain holes.

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A031140 Position of rightmost 0 in 2^n increases.

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A031141 Position of rightmost digit 0 in 2^A031140(n).

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Mathematica

PARI

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