A055254 -id:A055254 - cp's OEIS frontend

A034887 Number of digits in 2^n.

1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22

Offset: 0

N. J. A. Sloane

The sequence consists of the positive integers, each appearing 3 or 4 times. - M. F. Hasler, Oct 08 2016

T. D. Noe, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Mersenne Number

Cf. A055253, A055254.
Cf. A000079, A055642.
See A125117 for the sequence of first differences.

[#Intseq(2^n): n in [0..100] ]; // Vincenzo Librandi, Jun 23 2015

seq(floor(n*ln(2)/ln(10))+1, n=0..100); # Jaap Spies, Dec 11 2003

Table[Length[IntegerDigits[2^n]], {n, 0, 100}] (* T. D. Noe, Feb 11 2013 *)
IntegerLength[2^Range[0,80]] (* Harvey P. Dale, Jul 28 2017 *)

A034887(n)=n*log(2)\log(10)+1 \\ or: { a(n)=#digits(1<M. F. Hasler, Oct 08 2016

def a(n): return len(str(1 << n))
print([a(n) for n in range(73)]) # Michael S. Branicky, Dec 23 2022

a(n) = floor(n*log_10(2)) + 1. E.g., a(10)=4 because 2^10 = 1024 and floor(10*log_10(2)) + 1 = 3 + 1 = 4. - Jaap Spies, Dec 11 2003

a(n) = A055642(2^n) = A055642(A000079(n)).

A055253 Number of even digits in 2^n.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 4, 3, 2, 3, 3, 2, 2, 5, 5, 4, 3, 4, 6, 3, 3, 6, 4, 6, 4, 5, 7, 6, 4, 4, 4, 5, 4, 7, 5, 4, 5, 7, 9, 8, 8, 8, 7, 8, 6, 10, 8, 7, 7, 9, 9, 6, 8, 8, 11, 11, 9, 12, 10, 10, 10, 13, 9, 8, 8, 10, 16, 15, 10, 13, 8, 7, 12, 12, 14, 13, 12, 15, 11, 12, 14, 10, 14, 16, 14, 16

Offset: 0

Asher Auel, May 05 2000

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A055254, A034887.

A055253 := proc(val) local i, j, k, n; n := 2^val; j := 0; k := floor(ln(n)/ln(10))+1; for i from 1 to k do if (n mod 10) mod 2 = 0 then j := j+1 fi; n := floor(n/10); od; RETURN(j); end: seq(A055253(n),n=0..110); # Jaap Spies, Dec 30 2003

Table[Length@ Select[IntegerDigits[2^n], EvenQ], {n, 0, 120}] (* or *)
Table[Total@ Pick[DigitCount[2^n], {0, 1, 0, 1, 0, 1, 0, 1, 0, 1}, 1], {n, 0, 120}] (* Michael De Vlieger, May 01 2016 *)
Count[IntegerDigits[#],?EvenQ]&/@(2^Range[0,100]) (* _Harvey P. Dale, Mar 25 2020 *)

a(n) = #select(x->(x % 2) == 0, digits(2^n)); \\ Michel Marcus, May 01 2016

def a(n): return sum(1 for d in str(1<Michael S. Branicky, Dec 23 2022

More terms from Jaap Spies, Dec 30 2003

A272896 Difference between the number of odd and even digits in the decimal expansion of 2^n.

Original entry on oeis.org

1, -1, -1, -1, 0, 0, -2, -1, -1, 1, -2, -4, -2, 0, -1, -1, 1, 2, -4, -4, -1, 1, -1, -5, 2, 2, -4, 1, -3, 1, 0, -4, -2, 2, 3, 3, 1, 4, -2, 2, 5, 3, -1, -5, -2, -2, -2, 1, -1, 3, -4, 0, 2, 2, -1, -1, 5, 2, 2, -4, -3, 1, -5, -1, 0, 0, -6, 3, 5, 5, 2, -10, -8, 2, -3, 7, 9, 0, 0

Offset: 0

Seiichi Manyama, May 09 2016

All vanishing entries are a(A272898(k)) = 0, k >= 1. - Wolfdieter Lang, May 24 2016

			2^10 = 1024, 2^11 = 2048, 2^12 = 4096, 2^13 = 8192.
So a(10) = 1 - 3 = -2, a(11) = 0 - 4 = -4, a(12) = 1 - 3 = -2, a(13) = 2 - 2 = 0.

Indranil Ghosh, Table of n, a(n) for n = 0..10000

Cf. A000079, A055253, A055254, A196563, A196564, A272898.

Table[Count[#, ?OddQ] - Count[#, ?EvenQ] &@ IntegerDigits[2^n], {n, 0, 100}] (* Michael De Vlieger, May 09 2016 *)

a(n) = #select(x -> x%2, digits(2^n)) - #select(x -> !(x%2), digits(2^n));
for(n=0, 78, print1(a(n),", ")) \\ Indranil Ghosh, Mar 13 2017

def A272896(n):
    x=y=0
    for i in str(2**n):
        if int(i)%2: x+=1
        else: y+=1
    return x - y # Indranil Ghosh, Mar 13 2017

def a(n)
  str = (2 ** n).to_s
  str.size - str.split('').map(&:to_i).select{|i| i % 2 == 0}.size * 2
end
(0..n).each{|i| p a(i)}

a(n) = A055254(n) - A055253(n) = A196564(2^n) - A196563(2^n). - Indranil Ghosh, Mar 13 2017

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A034887 Number of digits in 2^n.

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A055253 Number of even digits in 2^n.

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A272896 Difference between the number of odd and even digits in the decimal expansion of 2^n.

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