A343181
Binary word formed from first 2^n-1 terms of paper-folding sequence A014577.
Original entry on oeis.org
1, 110, 1101100, 110110011100100, 1101100111001001110110001100100, 110110011100100111011000110010011101100111001000110110001100100
Offset: 1
- Chandler Davis and Donald E. Knuth, Number Representations and Dragon Curves -- I and II, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. Reprinted in Donald E. Knuth, Selected Papers on Fun and Games, CSLI Publications, 2010, pages 571-614.
- Rémy Sigrist and N. J. A. Sloane, Two-Dimensional Paper-Folding, Manuscript in preparation, May 2021.
- Chandler Davis and Donald E. Knuth, Number Representations and Dragon Curves, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. [Cached copy, with permission]
When converted to base 10 we get
A337580.
A343183
A343182(n) converted from base 2 to base 10.
Original entry on oeis.org
0, 4, 100, 27748, 1826909284, 7846656366854040676, 144745261873314177466380711909411548260, 49254260310842419635956203183145610297181518175722645092459215139793457671268
Offset: 0
A348162
a(n) is the previous term in binary with 0's and 1's put alternatingly before each digit, starting with 0.
Original entry on oeis.org
0, 0, 2, 38, 9782, 641083190, 2753431335706502966, 50791843174310108512166439539235563318, 17283568615631356151658578642396687258566665947274335391075779120894446085942
Offset: 0
a(2) = 0010;
a(3) = (0010 + 0101 -> 00100110);
a(4) = (00100110 + 01010101 = 0010011000110110).
Full explanation:
Say we have the term 0010.
We get an equal length binary number of alternating 0s and 1s.
In this case it would be 0101, and we interlace them like so:
0 1 0 1
0010 + 0101 -> 0 0 1 0 -> 00100110
-
a(n) = my(ret=0,s=1); for(i=2,n, ret += 1<Kevin Ryde, Nov 19 2021
-
def combine(a,b):
c = ''
for i in range(max(len(a),len(b))*2):
if i%2 == 0:
if len(a) > i/2:
c += (a[int(i/2)])
else:
if len(b) > i/2:
c += (b[int(i/2)])
return c
x = '0'
while True:
x = combine(combine(len(x)*'0',len(x)*'1')[:len(x)],x)
-
from itertools import islice
def A348162(): # generator of terms
s = '0'
while True:
yield int(s,2)
s = ''.join(x+y for x, y in zip('01'*((len(s)+1)//2),s))
A348162_list = list(islice(A348162(),9)) # Chai Wah Wu, Nov 19 2021
Showing 1-3 of 3 results.
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