A358168
First n-digit number to occur in Van Eck's Sequence (A181391).
Original entry on oeis.org
0, 14, 131, 1024, 10381, 100881, 1014748, 10001558, 100246289, 1000943528, 10010107437
Offset: 1
a(2) = 14 because 14 is the first 2-digit number occurring in A181391.
-
nn = 2^20; q[] = False; q[0] = True; a[] = 0; c[] = -1; c[0] = 2; m = 1; {0}~Join~Rest@ Reap[Do[j = c[m]; a[n] = m; c[m] = n; m = 0; If[j > 0, m = n - j]; If[! q[#2], Sow[#1]; q[#2] = True] & @@ {a[n], IntegerLength[a[n]]}, {n, 3, nn}] ][[-1, -1]] (* _Michael De Vlieger, Nov 05 2022 *)
-
from itertools import count
def A358168(n):
b, bdict, k = 0, {0:(1,)},10**(n-1) if n > 1 else 0
for m in count(2):
if b >= k:
return b
if len(l := bdict[b]) > 1:
b = m-1-l[-2]
if b in bdict:
bdict[b] = (bdict[b][-1],m)
else:
bdict[b] = (m,)
else:
b = 0
bdict[0] = (bdict[0][-1],m) # Chai Wah Wu, Nov 05 2022
A358258
First n-bit number to appear in Van Eck's sequence (A181391).
Original entry on oeis.org
0, 2, 6, 9, 17, 42, 92, 131, 307, 650, 1024, 2238, 4164, 8226, 17384, 33197, 67167, 133549, 269119, 525974, 1055175, 2111641, 4213053, 8444257, 16783217, 33601813, 67405064, 134239260, 268711604, 538400994, 1076155844, 2152693259, 4299075300, 8594396933, 17203509931
Offset: 1
First terms written in binary, substituting "." for 0 to enhance the pattern of 1's.
n a(n) a(n)_2
-------------------------------------
1 0 .
2 2 1.
3 6 11.
4 9 1..1
5 17 1...1
6 42 1.1.1.
7 92 1.111..
8 131 1.....11
9 307 1..11..11
10 650 1.1...1.1.
11 1024 1..........
12 2238 1...1.11111.
13 4164 1.....1...1..
14 8226 1.......1...1.
15 17384 1....11111.1...
16 33197 1......11.1.11.1
17 67167 1.....11..1.11111
18 133549 1.....1..11.1.11.1
19 269119 1.....11.11..111111
20 525974 1........11.1..1.11.
21 1055175 1.......11..111...111
22 2111641 1.......111...1..11..1
23 4213053 1.......1..1..1..1111.1
24 8444257 1.......11.11..1.11....1
-
nn = 2^20; q[] = False; q[0] = True; a[] = 0; c[_] = -1; c[0] = 2; m = 1; {0}~Join~Rest@ Reap[Do[j = c[m]; k = m; c[m] = n; m = 0; If[j > 0, m = n - j]; If[! q[#], Sow[k]; q[#] = True] & @ IntegerLength[k, 2], {n, 3, nn}] ][[-1, -1]]
-
from itertools import count
def A358258(n):
b, bdict, k = 0, {0:(1,)},1< 1 else 0
for m in count(2):
if b >= k:
return b
if len(l := bdict[b]) > 1:
b = m-1-l[-2]
if b in bdict:
bdict[b] = (bdict[b][-1],m)
else:
bdict[b] = (m,)
else:
b = 0
bdict[0] = (bdict[0][-1],m) # Chai Wah Wu, Nov 06 2022
A358259
Positions of the first n-bit number to appear in Van Eck's sequence (A181391).
Original entry on oeis.org
1, 5, 10, 24, 41, 52, 152, 162, 364, 726, 1150, 2451, 4626, 9847, 18131, 36016, 71709, 143848, 276769, 551730, 1086371, 2158296, 4297353, 8607525, 17159741, 34152001, 68194361, 136211839, 271350906, 541199486, 1084811069, 2165421369, 4331203801, 8643518017, 17303787585
Offset: 1
First terms written in binary, substituting "." for 0 to enhance the pattern of 1's.
n a(n) a(n)_2
-------------------------------------
1 1 1
2 5 1.1
3 10 1.1.
4 24 11...
5 41 1.1..1
6 52 11.1..
7 152 1..11...
8 162 1.1...1.
9 364 1.11.11..
10 726 1.11.1.11.
11 1150 1...111111.
12 2451 1..11..1..11
13 4626 1..1....1..1.
14 9847 1..11..111.111
15 18131 1...11.11.1..11
16 36016 1...11..1.11....
17 71709 1...11......111.1
18 143848 1...11...1111.1...
19 276769 1....111..1..1....1
20 551730 1....11.1.11..11..1.
21 1086371 1....1..1..111.1...11
22 2158296 1.....111.111.11.11...
23 4297353 1.....11..1..1.1...1..1
24 8607525 1.....11.1.1.111..1..1.1
etc.
-
nn = 2^20; q[] = False; q[0] = True; a[] = 0; c[_] = -1; c[0] = 2; m = 1; {1}~Join~Rest@ Reap[Do[j = c[m]; k = m; c[m] = n; m = 0; If[j > 0, m = n - j]; If[! q[#], Sow[n]; q[#] = True] & @ IntegerLength[k, 2], {n, 3, nn}] ][[-1, -1]]
-
from itertools import count
def A358259(n):
b, bdict, k = 0, {0:(1,)},1< 1 else 0
for m in count(2):
if b >= k:
return m-1
if len(l := bdict[b]) > 1:
b = m-1-l[-2]
if b in bdict:
bdict[b] = (bdict[b][-1],m)
else:
bdict[b] = (m,)
else:
b = 0
bdict[0] = (bdict[0][-1],m) # Chai Wah Wu, Nov 06 2022
Showing 1-3 of 3 results.
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