A007088 -id:A007088 - cp's OEIS frontend

A007094 Numbers in base 8.

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 100, 101, 102, 103, 104, 105, 106, 107, 110, 111

Offset: 0

N. J. A. Sloane, Robert G. Wilson v

Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §2.8 Binary, Octal, Hexadecimal, p. 64.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Nathaniel Johnston, Table of n, a(n) for n = 0..10000
Wikipedia, Octal.
Robert G. Wilson v, Letter to N. J. A. Sloane, Sep. 1992
Index entries for 10-automatic sequences.

Cf. A057104; A000042 (base 1), A007088 (base 2), A007089 (base 3), A007090 (base 4), A007091 (base 5), A007092 (base 6), A007093 (base 7), A007095 (base 9).

a007094 0 = 0
a007094 n = 10 * a007094 n' + m where (n', m) = divMod n 8
-- Reinhard Zumkeller, Aug 29 2013

A007094 := proc(n) local l: if(n=0)then return 0: fi: l:=convert(n,base,8): return op(convert(l,base,10,10^nops(l))): end: seq(A007094(n), n=0..66); # Nathaniel Johnston, May 06 2011

Table[FromDigits[IntegerDigits[n, 8]], {n, 0, 70}]

a(n)=if(n<1,0,if(n%8,a(n-1)+1,10*a(n/8)))

apply( A007094(n)=fromdigits(digits(n,8)), [0..77]) \\ M. F. Hasler, Nov 18 2019

def a(n): return int(oct(n)[2:])
print([a(n) for n in range(74)]) # Michael S. Branicky, Jun 28 2021

a(0) = 0; a(n) = 10*a(n/8) if n == 0 (mod 8); a(n) = a(n-1) + 1 otherwise. - Benoit Cloitre, Dec 22 2002

G.f.: sum(d>=0, 10^d*(x^(8^d) +2*x^(2*8^d) +3*x^(3*8^d) +4*x^(4*8^d) +5*x^(5*8^d) +6*x^(6*8^d) +7*x^(7*8^d)) * (1-x^(8^d)) / ((1-x^(8^(d+1)))*(1-x))). - Robert Israel, Aug 03 2014

A007093 Numbers in base 7.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 54, 55, 56, 60, 61, 62, 63, 64, 65, 66, 100, 101, 102, 103, 104, 105, 106, 110, 111, 112, 113, 114, 115, 116, 120

Offset: 0

N. J. A. Sloane, Robert G. Wilson v

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See p. 67.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Nathaniel Johnston, Table of n, a(n) for n = 0..10000
R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992
Index entries for 10-automatic sequences.

Cf. A000042, A007088, A007089, A007090, A007091, A007092, A007094, A007095.

A007093 := proc(n) local l: if(n=0)then return 0: fi: l:=convert(n,base,7): return op(convert(l,base,10,10^nops(l))): end: seq(A007093(n),n=0..63); # Nathaniel Johnston, May 06 2011

Table[ FromDigits[ IntegerDigits[n, 7]], {n, 0, 66}]

a(n)=if(n<1,0,if(n%7,a(n-1)+1,10*a(n/7)))

a(n) = fromdigits(digits(n, 7)); \\ Michel Marcus, Aug 12 2018

a(0) = 0, a(n) = 10*a(n/7) if n==0 (mod 7), a(n) = a(n-1)+1 otherwise. - Benoit Cloitre, Dec 22 2002

A007092 Numbers in base 6.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 55, 100, 101, 102, 103, 104, 105, 110, 111, 112, 113, 114, 115, 120, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 140, 141, 142, 143, 144, 145

Offset: 0

N. J. A. Sloane, Robert G. Wilson v

Nonnegative integers with no decimal digits > 5. - Karol Bacik, Sep 25 2012

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Nathaniel Johnston, Table of n, a(n) for n = 0..10000
Wikipedia, Senary
R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992
Index entries for 10-automatic sequences.

Cf. A000042 (base 1), A007088 (base 2), A007089 (base 3), A007090 (base 4), A007091 (base 5), A007093 (base 7), A007094 (base 8), A007095 (base 9).

a007092 0 = 0
a007092 n = 10 * a007092 n' + m where (n', m) = divMod n 6
-- Reinhard Zumkeller, Mar 06 2015

A007092 := proc(n) local l: if(n=0)then return 0: fi: l:=convert(n,base,6): return op(convert(l,base,10,10^nops(l))): end: seq(A007092(n),n=0..59); # Nathaniel Johnston, May 06 2011

Table[ FromDigits[ IntegerDigits[n, 6]], {n, 0, 65}]

a(n)=if(n%6,a(n-1)+1,if(n,10*a(n/6),0))  \\ corrected by Charles R Greathouse IV, Sep 25 2012

a(n)=n=digits(n,6);n[1]=Str(n[1]);eval(concat(n)) \\ Charles R Greathouse IV, Sep 25 2012

apply( A007092(n)=fromdigits(digits(n, 6)), [0..66]) \\ M. F. Hasler, Nov 18 2019

a(0)=0, a(n) = 10*a(n/6) if n==0 (mod 6), and a(n) = a(n-1)+1 otherwise. - Benoit Cloitre, Dec 22 2002

a(n) = Sum{d(i)*10^i: i=0,1,...,m}, where Sum{d(i)*6^i: i=1,2,...,m} = n, and d(i) in {0,1,...,5}. - Karol Bacik, Sep 25 2012

A029447 Numbers k that divide the (right) concatenation of all numbers <= k written in base 2 (most significant digit on left).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 16, 26, 32, 38, 40, 46, 64, 96, 128, 138, 192, 228, 256, 512, 640, 1024, 2048, 4096, 4192, 4766, 4790, 5142, 5952, 6144, 6866, 8122, 8192, 8448, 10240, 11283, 11392, 12288, 14780, 15360, 15744, 16384, 17408, 20841, 20866, 32768, 58496, 59104

Offset: 1

Olivier Gérard

All powers of 2 are in the sequence. - Chai Wah Wu, Nov 10 2014

Numbers k that divide A047778(k). - Michel Marcus, Nov 11 2014

			3 is in the sequence because the concatenation is 1 10 11, binary expansion of 27, that is divisible by 3.

Chai Wah Wu, Table of n, a(n) for n = 1..54

Cf. A007088, A047778.

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Select[Range[2^13], Mod[FromDigits[Flatten[IntegerDigits[#, 2] & /@ Range@ #], 2], #] == 0 &] (* Michael De Vlieger, Aug 29 2015 *)

lista(nn) = {vs = []; for (n=1, nn, vs = concat(vs, binary(n)); val = subst(Pol(vs), x, 2); if (val % n == 0, print1(n, ", ")););} \\ Michel Marcus, Nov 11 2014

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
More terms from David W. Wilson
a(47)-a(49) from Chai Wah Wu, Nov 10 2014

A063171 Dyck language interpreted as binary numbers in ascending order.

Original entry on oeis.org

0, 10, 1010, 1100, 101010, 101100, 110010, 110100, 111000, 10101010, 10101100, 10110010, 10110100, 10111000, 11001010, 11001100, 11010010, 11010100, 11011000, 11100010, 11100100, 11101000, 11110000, 1010101010, 1010101100, 1010110010, 1010110100, 1010111000

Offset: 0

Reinhard Zumkeller, Jul 09 2001

a(n) is the binary expansion of A014486(n). - Joerg Arndt, Feb 27 2013
Replacing "1" by "(" and "0" by ")" yields well-formed bracket expressions (the first term being the empty string)
  , (), ()(), (()), ()()(), ()(()), (())(), (()()), ((())), ()()()(), ()()(()), ()(())(), ()(()()), ()((())), (())()(), (())(()), (()())(), (()()()), (()(())), ((()))(), ((())()), ((()())), (((()))), ()()()()(), ()()()(()), ()()(())(), ()()(()()), ()()((())), ()(())()(), ()(())(()), ()(()())(), ()(()()()), ()(()(())), ()((()))(), ()((())()), ()((()())), ()(((()))), (())()()(), (())()(()), (())(())(), (())(()()), (())((())), (()())()(), (()())(()), (()()())(), (()()()()), (()()(())), (()(()))(), (()(())()), (()(()())), (()((()))), ((()))()(), ((()))(()), ((())())(), ((())()()), ((())(())), ((()()))(), ((()())()), ((()()())), ((()(()))), (((())))(), (((()))()), (((())())), (((()()))), ((((()))))
The term a(0)=0 stands for the empty string. - Joerg Arndt, Feb 27 2013

			s -> ss -> 1s0s -> 11s00s -> 111000s -> 11100010

Donald E. Knuth, The Art of Computer Programming, Vol. 4A: Combinatorial Algorithms, Part 1, Addison-Wesley, 2011, Section 7.2.1.6, pp. 443 (Algorithm P).

Paolo Xausa, Table of n, a(n) for n = 0..23713 (terms 0..2055 from Reinhard Zumkeller)
Gennady Eremin, Dynamics of balanced parentheses, lexicographic series and Dyck polynomials, arXiv:1909.07675 [math.CO], 2019.
FindStat - Combinatorial Statistic Finder, Dyck paths.
Antti Karttunen, Illustration of initial terms up to size n=7.
Antti Karttunen, Catalan Automorphisms.
Zoltán Kása, Generating and ranking of Dyck words, arXiv:1002.2625 [cs.DM], Feb 2010.
Peter Luschny, A Python implementation of Knuth's algorithms P and U.
R. J. Mathar, Topologically Distinct Sets of Non-intersecting Circles in the Plane, arXiv:1603.00077 [math.CO], 2016.
Indranil Ghosh, Python program for computing this sequence.
Paolo Xausa, A Mathematica implementation of Knuth's algorithms P and U.

Cf. A007088, A071153.

A014486 gives these terms as converted from decimal to binary system.

import Data.Set (singleton, deleteFindMin, union, fromList)
newtype Word = Word String deriving (Eq, Show, Read)
instance Ord Word where
   Word us <= Word vs | length us == length vs = us <= vs
                      | otherwise              = length us <= length vs
a063171 n = a063171_list !! (n-1)
a063171_list = dyck $ singleton (Word "S") where
   dyck s | null ws   = (read w :: Integer) : dyck s'
          | otherwise = dyck $ union s' (fromList $ concatMap gen ws)
          where ws = filter ((== 'S') . head . snd) $
                            map (`splitAt` w) [0..length w - 1]
                (Word w, s') = deleteFindMin s
   gen (us,vs) = map (Word . (us ++) . (++ tail vs)) ["10", "1S0", "SS"]
-- Reinhard Zumkeller, Mar 09 2011

seq(convert(d, binary), d in select(isA014486, [seq(0..640)]));  # Peter Luschny, Mar 13 2024

balancedQ[0] = True; balancedQ[n_] := (s = 0; Do[s += If[b == 1, 1, -1]; If[s < 0, Return[False]], {b, IntegerDigits[n, 2]}]; Return[s == 0]); FromDigits /@ IntegerDigits[ Select[Range[0, 684], balancedQ], 2] (* Jean-François Alcover, Jul 24 2013 *)
(* Uses Algorithm P from Knuth's TAOCP section 7.2.1.6 - see References and Links. *)
alist[n_] := Block[{a = Flatten[Table[{1, 0}, n]], m = 2*n - 1, j, k},
    FromDigits /@ Reap[
    While[True,
        Sow[a]; a[[m]] = 0;
        If[a[[m - 1]] == 0,
            a[[--m]] = 1, j = m - 1; k = 2*n - 1;
            While[j > 1 && a[[j]] == 1, a[[j--]] = 0; a[[k]] = 1; k -= 2];
            If[j == 1, Break[]];
            a[[j]] = 1; m = 2*n - 1]
    ]][[2, 1]]];
Join[{{0}, {10}}, Array[alist, 4, 2]] (* Paolo Xausa, Mar 15 2024 *)

a_rows(N) = my(a=Vec([[0]], N)); for(r=1, N-1, my(b=a[r], c=List()); foreach(b, t, for(i=1, if(t, valuation(t, 10), 0)+1, listput(~c, t*100+10^i))); a[r+1]=Vec(c)); a; \\ Ruud H.G. van Tol, Jun 02 2024

def A063171_list(limit):
    return [0] + [int(bin(k)[2::]) for k in range(1, limit) if is_A014486(k)]
print(A063171_list(700))  # Peter Luschny, Jul 30 2022

from itertools import count, islice
from sympy.utilities.iterables import multiset_permutations
def A063171_gen(): # generator of terms
    yield 0
    for l in count(1):
        for s in multiset_permutations('0'*l+'1'*(l-1)):
            c, m = 0, (l<<1)-1
            for i in range(m):
                if s[i] == '1':
                    c += 2
                if cA063171_list = list(islice(A063171_gen(),30)) # Chai Wah Wu, Nov 28 2023

Chomsky-2 grammar with axiom s, terminal alphabet {0, 1} and three rules s -> ss, s -> 1s0, s -> 10.
a(n) = A071152(n)/2.
a(n) = A007088(A014486(n)).

a(0)=0 prepended by Joerg Arndt, Feb 27 2013

A029471 Numbers k that divide the (left) concatenation of all numbers <= k written in base 2 (most significant digit on left).

Original entry on oeis.org

1, 85, 145, 245, 1189, 356717, 19590671, 35741759, 791822369, 25313027035

Offset: 1

Olivier Gérard

No other terms below 3*10^10.

Index entries for related sequences

Cf. A007088.

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

b = 2; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[#, b], c], b], #] &] (* Robert Price, Mar 12 2020 *)

from itertools import count
def a029471():
    total = 0
    power_of_two = 1
    index_of_two = 0
    length_of_string = 0
    for n in count(1):
        total += (n<Christian Perfect, Feb 07 2014

def concat_mod(base, k, mod): ...  # See A029479
for k in range(1, 3*10**10):
  if concat_mod(2, k, k) == 0: print(k) # Jason Yuen, Mar 24 2024

One more term from Larry Reeves (larryr(AT)acm.org), Dec 03 2001
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(7)-a(8) from Max Alekseyev, May 12 2011
a(9)-a(10) from Jason Yuen, Mar 24 2024

A020449 Primes whose greatest digit is 1.

Original entry on oeis.org

11, 101, 10111, 101111, 1011001, 1100101, 10010101, 10011101, 10100011, 10101101, 10110011, 10111001, 11000111, 11100101, 11110111, 11111101, 100100111, 100111001, 101001001, 101001011, 101100011, 101101111, 101111011, 101111111

Offset: 1

David W. Wilson

Primes which are the sums of distinct powers of 10. - Amarnath Murthy, Nov 19 2002
Subsequence of A007088. - Michel Marcus, Dec 18 2015
These numbers are called Anti-Yarborough prime numbers in the Prime Glossary. - Randy L. Ekl, Jan 19 2019

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
C. K. Caldwell, The Prime Glossary, Yarborough prime.
FactorDB, Concatenation of first 35 terms is prime
Index to entries for primes with digits in a given set

Subsequence of A036953.

Cf. A007088, A036952.

[p: p in PrimesUpTo(101111111) | Set(Intseq(p)) subset [0,1]]; // Vincenzo Librandi, Jul 27 2012

N:= 10: # to get all entries with <= N digits
S:= {}:
for d from 1 to N-1 do
  S:= S union select(isprime,map(`+`,map(convert,combinat[powerset]({seq(10^i,i=0..d-1)}),`+`),10^d));
od:
S; # if using Maple 11 or earlier, uncomment the next line
# sort(convert(%,list)); # Robert Israel, May 04 2015

Select[FromDigits/@Tuples[{0,1},16],PrimeQ] (* Hans Havermann, May 12 2025 *)

is(n)=isprime(n)&&vecmax(digits(n))==1 \\ Charles R Greathouse IV, Jul 01 2013

from sympy import isprime
A020449_list = [n for n in (int(format(m,'b')) for m in range(1,2**10)) if isprime(n)] # Chai Wah Wu, Dec 17 2015

A054055 Largest digit of n.

Original entry on oeis.org

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

Offset: 0

Henry Bottomley, Apr 29 2000

A095815(n) = n + a(n). - Reinhard Zumkeller, Aug 23 2011
a(A007088(n)) = 1, n > 0; a(A136399(n)) > 1. - Reinhard Zumkeller, Apr 25 2012
a(n) = 9 for almost all n. Sum_{n < x} a(n) = 9x + O(.956^x). - Charles R Greathouse IV, Oct 02 2013

			a(12)=2 because 1 < 2.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

For bases 3 through 12 see A190592, A190593, A190594, A190595, A190596, A190597, A190598, A054055, A190599, A190600.

Cf. A054054.

a054055 = f 0 where
   f m x | x <= 9 = max m x
         | otherwise = f (max m d) x' where (x',d) = divMod x 10
-- Reinhard Zumkeller, Jun 20 2012, May 14 2011

[n eq 0 select 0 else Maximum(Intseq(n)): n in [0..104]]; // Bruno Berselli, Aug 24 2011

[seq(max(convert(n,base,10)),n=0..120)];

f[n_] := Sort[IntegerDigits[n]][[-1]]; Array[f, 105, 0] (* Alonso del Arte, May 14 2011 *) (* and revised by Robert G. Wilson v, Aug 24 2011 *)
Max/@IntegerDigits[Range[0,110]] (* Harvey P. Dale, Apr 17 2016 *)

a(n)=vecmax(eval(Vec(Str(n)))) \\ Charles R Greathouse IV, Jun 16 2011

a(n)=vecmax(digits(n)) \\ Charles R Greathouse IV, Oct 02 2013

def A054055(n): return max(int(d) for d in str(n)) # Chai Wah Wu, Jun 06 2022

A000042 Unary representation of natural numbers.

Original entry on oeis.org

1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, 111111111111111111, 1111111111111111111, 11111111111111111111

Offset: 1

N. J. A. Sloane

Or, numbers written in base 1.
If p is a prime > 5 then d_{a(p)} == 1 (mod p) where d_{a(p)} is a divisor of a(p). This also gives an alternate elementary proof of the infinitude of prime numbers by the fact that for every prime p there exists at least one prime of the form k*p + 1. - Amarnath Murthy, Oct 05 2002
11 = 1*9 + 2; 111 = 12*9 + 3; 1111 = 123*9 + 4; 11111 = 1234*9 + 5; 111111 = 12345*9 + 6; 1111111 = 123456*9 + 7; 11111111 = 1234567*9 + 8; 111111111 = 12345678*9 + 9. - Vincenzo Librandi, Jul 18 2010

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See pp. 57-58.
K. G. Kroeber, Mathematik der Palindrome; p. 348; 2003; ISBN 3 499 615762; Rowohlt Verlag; Germany.
D. Olivastro, Ancient Puzzles. Bantam Books, NY, 1993, p. 276.
Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 32.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

David Wasserman, Table of n, a(n) for n = 1..1000
Makoto Kamada, Factorizations of 11...11 (Repunit).
Amarnath Murthy, On the divisors of Smarandache Unary Sequence. Smarandache Notions Journal, Vol. 11, No. 1-2-3, Spring 2000, page 184.
Amarnath Murthy and Charles Ashbacher, Generalized Partitions and Some New Ideas on Number Theory and Smarandache Sequences, Hexis, Phoenix; USA 2005. See Section 2.12.
Index entries for linear recurrences with constant coefficients, signature (11,-10).
Index to divisibility sequences

Cf. A002275, A007088, A007089, A007090, A007091, A007092, A007093, A007094, A007095, A007908, A065444.

A000042 n = (10^n-1) `div` 9 -- James Spahlinger, Oct 08 2012
(Common Lisp) (defun a000042 (n) (truncate (expt 10 n) 9)) ; James Spahlinger, Oct 12 2012

[(10^n - 1)/9: n in [1..20]]; // G. C. Greubel, Nov 04 2018

a:= n-> parse(cat(1$n)):
seq(a(n), n=1..25);  # Alois P. Heinz, Mar 23 2018

Table[(10^n - 1)/9, {n, 1, 18}]
FromDigits/@Table[PadLeft[{},n,1],{n,20}] (* Harvey P. Dale, Aug 21 2011 *)

PARI
```
a(n)=if(n<0,0,(10^n-1)/9)
```

def a(n): return int("1"*n) # Michael S. Branicky, Jan 01 2021

[gaussian_binomial(n, 1, 10) for n in range(1, 19)]  # Zerinvary Lajos, May 28 2009

a(n) = (10^n - 1)/9.
G.f.: 1/((1-x)*(1-10*x)).
Binomial transform of A003952. - Paul Barry, Jan 29 2004
From Paul Barry, Aug 24 2004: (Start)
a(n) = 10*a(n-1) + 1, n > 1, a(1)=1. [Offset 1.]
a(n) = Sum_{k=0..n} binomial(n+1, k+1)*9^k. [Offset 0.] (End)
a(2n) - 2*a(n) = (3*a(n))^2. - Amarnath Murthy, Jul 21 2003
a(n) is the binary representation of the n-th Mersenne number (A000225). - Ross La Haye, Sep 13 2003
The Hankel transform of this sequence is [1,-10,0,0,0,0,0,0,0,0,...]. - Philippe Deléham, Nov 21 2007
E.g.f.: (exp(10*x) - exp(x))/9. - G. C. Greubel, Nov 04 2018
a(n) = 11*a(n-1) - 10*a(n-2). - Wesley Ivan Hurt, May 28 2021
a(n+m-2) = a(m)*a(n-1) - (a(m)-1)*a(n-2), n>1, m>0. - Matej Veselovac, Jun 07 2021
Sum_{n>=1} 1/a(n) = A065444. - Stefano Spezia, Jul 30 2024

More terms from Paul Barry, Jan 29 2004

A004676 Primes written in base 2.

Original entry on oeis.org

10, 11, 101, 111, 1011, 1101, 10001, 10011, 10111, 11101, 11111, 100101, 101001, 101011, 101111, 110101, 111011, 111101, 1000011, 1000111, 1001001, 1001111, 1010011, 1011001, 1100001, 1100101, 1100111, 1101011, 1101101, 1110001, 1111111, 10000011, 10001001

Offset: 1

N. J. A. Sloane

The only primes of binary weight 2 are the Fermat primes (only five are known: 11, 101, 10001, 100000001, 10000000000000001); the repunits base 2 are the Mersenne primes. - Daniel Forgues, Nov 07 2011

J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 3.

T. D. Noe, Table of n, a(n) for n = 1..1000
Chris Caldwell, The prime pages, The first 1000 primes.

Cf. A019434 Fermat primes (base 10), A000668 Mersenne primes (base 10).

Cf. A174332, A208238, A208241.

a004676 = a007088 . a000040  -- Reinhard Zumkeller, Aug 06 2012

FromDigits /@ IntegerDigits[ Prime[ Range[31]], 2] (* Robert G. Wilson v, Jun 30 2005 *)

a(n)=subst(Pol(binary(prime(n))), 'x, 10) \\ Charles R Greathouse IV, Mar 20 2013

a(n) = A007088(A000040(n)). - R. J. Mathar, Jun 03 2011

cp's OEIS Frontend

A007094 Numbers in base 8.

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A007093 Numbers in base 7.

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Maple

Mathematica

PARI

PARI

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A007092 Numbers in base 6.

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Maple

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PARI

PARI

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A029447 Numbers k that divide the (right) concatenation of all numbers <= k written in base 2 (most significant digit on left).

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Mathematica

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A063171 Dyck language interpreted as binary numbers in ascending order.

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Haskell

Maple

Mathematica

PARI

Python

Python

Formula

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A029471 Numbers k that divide the (left) concatenation of all numbers <= k written in base 2 (most significant digit on left).

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