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.

A007881 Erroneous version of A001357 printed by mistake on back cover of Encyclopedia of Integer Sequences.

Original entry on oeis.org

1, 2, 4, 8, 18, 71
Offset: 0

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Author

Keywords

A364049 a(n) is the least k such that the base-n digits of 2^k are not all distinct.

Original entry on oeis.org

2, 2, 4, 5, 6, 3, 6, 11, 16, 14, 11, 12, 8, 4, 8, 15, 16, 12, 16, 18, 9, 17, 15, 14, 24, 13, 16, 15, 10, 5, 10, 19, 24, 14, 21, 15, 18, 15, 19, 17, 17, 28, 18, 12, 24, 23, 31, 24, 31, 20, 26, 44, 35, 33, 25, 18, 36, 14, 14, 18, 12, 6, 12, 23, 45, 37, 38, 24, 20, 35, 36, 26, 51, 31, 33, 47, 34, 34
Offset: 2

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Author

Robert Israel, Jul 03 2023

Keywords

Examples

			a(10) = 16 because 2^16 = 65536 does not have all distinct digits in base 10, while 2^k does have all distinct digits for 1 <= k <= 15.

Links

Crossrefs

Cf. A004642, A004643, A000866, A004645, A004646, A004647, A001357, A000079, A011557, A364052, A364089.

Programs

  • Maple
    f:= proc(n) local k,L;
  for k from 2 do
    L:= convert(2^k,base,n);
    if nops(L) <> nops(convert(L,set)) then return k fi
  od;
end proc:
map(f, [$2..100]);
  • Python
    from itertools import count
from sympy.ntheory import digits
def a(n): return next(k for k in count(2) if len(set(d:=digits(1<Michael S. Branicky, Jul 05 2023

A309908 a(n) is 2^n represented in bijective base-9 numeration.

Original entry on oeis.org

1, 2, 4, 8, 17, 35, 71, 152, 314, 628, 1357, 2725, 5551, 12212, 24424, 48848, 98797, 218715, 438531, 878162, 1867334, 3845668, 7792447, 16694895, 34499911, 69121922, 149243944, 299487988, 619987187, 1342185385, 2684381781, 5478773672, 11968657454, 24148425918
Offset: 0

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Author

Alois P. Heinz, Aug 21 2019

Keywords

Comments

Differs from A001357 first at n = 16: a(16) = 98797 < 108807 = A001357(16).

Examples

			a(10) =  1357_bij9 =       9*(9*(9*1+3)+5)+7 =  1024 = 2^10.
a(16) = 98797_bij9 = 9*(9*(9*(9*9+8)+7)+9)+7 = 65536 = 2^16.

Links

Crossrefs

Cf. A000079, A001357, A047855, A052382, A093135, A214676, A325203.

Programs

  • Maple
    b:= proc(n) local d, l, m; m:= n; l:= "";
      while m>0 do d:= irem(m, 9, 'm');
        if d=0 then d:=9; m:= m-1 fi; l:= d, l
      od; parse(cat(l))
    end:
a:= n-> b(2^n):
seq(a(n), n=0..33);

Formula

a(n) = A052382(2^n) = A052382(A000079(n)).

A364089 a(n) is the greatest k such that the base-n digits of 2^k are all distinct.

Original entry on oeis.org

1, 1, 3, 4, 5, 8, 5, 10, 29, 19, 19, 19, 16, 18, 7, 43, 41, 37, 45, 39, 55, 33, 43, 60, 35, 61, 56, 50, 44, 69, 9, 64, 44, 80, 43, 88, 53, 71, 56, 68, 59, 78, 76, 74, 95, 109, 111, 81, 86, 136, 117, 75, 98, 83, 84, 99, 104, 116, 95, 118, 60, 81, 11, 119, 119, 172, 140, 97, 105, 113, 93, 122, 92
Offset: 2

Views

Author

Robert Israel, Jul 04 2023

Keywords

Comments

a(n) <= log_2(A062813(n)).

Examples

			a(10) = 29 because all decimal digits of 2^29 = 536870912 are distinct.

Crossrefs

Cf. A004642, A004643, A000866, A004645, A004646, A004647, A001357, A000079, A364049.

Programs

  • Maple
    f:= proc(b) local M,k,L;
  M:= b^b - (b^b-b)/(b-1)^2;
  for k from ilog2(M) to 1 by -1 do
    L:= convert(2^k,base,b);
    if nops(L) = nops(convert(L,set)) then return k fi
  od
end proc:
map(f, [$2..100]);
  • Python
    from sympy.ntheory.factor_ import digits
def A364089(n):
    m = 1<<(l:=((r:=n**n)-(r-n)//(n-1)**2).bit_length()-1)
    while len(d:=digits(m,n)[1:]) > len(set(d)):
        l -= 1
        m >>= 1
    return l # Chai Wah Wu, Jul 07 2023
Showing 1-4 of 4 results.

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