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 1-4 of 4 results.

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

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

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

Examples

			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)

Links

  • Eric Weisstein's World of Mathematics, Zero.

Crossrefs

Cf. A031141, A031142, A031143.

Programs

  • Mathematica
    best = 0;
Select[Range[10000],
 If[(t = First@
       First@StringPosition[StringReverse@ToString@(2^#), "0"]) >
best, best = t; True] &] (* 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&&(m=j)&&print1(k",")||break))) \\ M. F. Hasler, Jun 21 2018

Extensions

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

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

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 1-4 of 4 results.

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