cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Views

Author

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

Keywords

Comments

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

Links

  • Eric Weisstein's World of Mathematics, Zero.

Crossrefs

Cf. A031140, A031142, A031143.

Programs

  • Mathematica
    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 *)
  • PARI
    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

Extensions

More terms from Dan Hoey

A031155 a(n) = 2^A031140(n).

Original entry on oeis.org

1024, 1048576, 1073741824, 1099511627776, 70368744177664, 295147905179352825856, 9903520314283042199192993792, 39614081257132168796771975168, 680564733841876926926749214863536422912, 95780971304118053647396689196894323976171195136475136, 862718293348820473429344482784628181556388621521298319395315527974912
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Powers of 2 such that there is an increasing number of nonzero digits after the rightmost digit '0'.

Crossrefs

Cf. A031140, A031156.

Extensions

Typo in title corrected by Sean A. Irvine, Apr 11 2020

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

Original entry on oeis.org

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

Views

Author

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

Keywords

Comments

"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.

Links

Crossrefs

Cf. A031140, A031141, A031142, A031143.

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

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

Keywords

Comments

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

Crossrefs

Cf. A031140, A031141, A031142, A031143.

Programs

  • Mathematica
    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 *)

Extensions

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

A266568 a(n) = smallest k such that 2^k ends in a string of exactly n nonzero digits.

Original entry on oeis.org

0, 4, 7, 13, 14, 18, 50, 24, 27, 31, 34, 37, 68, 93, 49, 51, 116, 214, 131, 155, 67, 72, 76, 77, 81, 86, 149, 498, 154, 286, 359, 866, 1225, 329, 664, 129, 573, 176, 655, 820, 571, 434, 1380, 475, 1260, 2251, 6015, 3066, 1738, 2136, 2297, 432, 665, 229, 1899
Offset: 1

Views

Author

Jon E. Schoenfield, Jan 01 2016

Keywords

Comments

Since 2^a(n) must have at least n digits, a(n) >= (n-1)*log_2(10).
The 26-digit number 2^86 = 77371252455336267181195264 is almost certainly the largest power of 2 that contains no zero digit.
A notably low local minimum occurs at a(36) = 129, which is less than a(n) for all n > 26.
A notably high local maximum occurs at a(122) = 11267047.

Examples

			2^0 = 1 is the smallest power of 2 ending in a string ("1") of exactly 1 nonzero digit, so a(1) = 0.
2^4 = 16 is the smallest power of 2 ending in a string ("16") of exactly 2 nonzero digits, so a(2) = 4.
2^50 = 1125899906842624 is the smallest power of 2 ending in a string ("6842624") of exactly 7 nonzero digits, so a(7) = 50.
The last 7 digits of 2^24 = 16777216 -- i.e., "6777216" -- are also nonzero, but so is the preceding digit, so 2^24 ends in a string of exactly 8 nonzero digits. Since no smaller power of 2 ends in exactly 8 nonzero digits, a(8) = 24.

Crossrefs

Cf. A007377, A031140, A031141, A031142, A031143, A181611.
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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