A018900 -id:A018900 - cp's OEIS frontend

A227092 Numbers whose base-7 sum of digits is 7.

13, 19, 25, 31, 37, 43, 55, 61, 67, 73, 79, 85, 91, 103, 109, 115, 121, 127, 133, 151, 157, 163, 169, 175, 199, 205, 211, 217, 247, 253, 259, 295, 301, 349, 355, 361, 367, 373, 379, 385, 397, 403, 409, 415, 421, 427, 445, 451, 457, 463, 469, 493, 499, 505

Offset: 1

Tom Edgar, Sep 01 2013

All of the entries are odd.
Subsequence of A016921. - Michel Marcus, Sep 03 2013
In general, the set of numbers with sum of base-b digits equal to b is a subset of { (b-1)*k + 1; k = 2, 3, 4, ... }. - M. F. Hasler, Dec 23 2016

			The 7-ary expansion of 13 is (1,6), which has sum of digits 7.
The 7-ary expansion of 103 is (2,0,5), which has sum of digits 7.
10 is not on the list since the 7-ary expansion of 10 is (1,3), which has sum of digits 4 not 7.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A018900, A187813.

Cf. A226636 (b = 3), A226969 (b = 4), A227062 (b = 5), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9), A052224 (b = 10).

Select[Range[600],Total[IntegerDigits[#,7]]==7&] (* Harvey P. Dale, Aug 18 2014 *)

select( is(n)=sumdigits(n,7)==7, [1..999]) \\ M. F. Hasler, Dec 23 2016

agen = A226636gen(sod=7, base=7) # generator of terms using code in A226636
print([next(agen) for n in range(1, 55)]) # Michael S. Branicky, Jul 10 2022

[i for i in [0..1000] if sum(Integer(i).digits(base=7))==7]

A227095 Numbers whose base-8 sum of digits is 8.

Original entry on oeis.org

15, 22, 29, 36, 43, 50, 57, 71, 78, 85, 92, 99, 106, 113, 120, 134, 141, 148, 155, 162, 169, 176, 197, 204, 211, 218, 225, 232, 260, 267, 274, 281, 288, 323, 330, 337, 344, 386, 393, 400, 449, 456, 519, 526, 533, 540, 547, 554, 561, 568, 582, 589, 596, 603

Offset: 1

Tom Edgar, Sep 01 2013

Subsequence of A016993. - Michel Marcus, Sep 03 2013

In general, the set of numbers with sum of base-b digits equal to b is a subset of { (b-1)*k + 1; k = 2, 3, 4, ... }. - M. F. Hasler, Dec 23 2016

			The 8-ary expansion of 15 is (1,7), which has sum of digits 8.
The 8-ary expansion of 78 is (1,1,6), which has sum of digits 8.
10 is not on the list since the 8-ary expansion of 10 is (1,2), which has sum of digits 3 not 8.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A018900, A187813.

Cf. A226636 (b = 3), A226969 (b = 4), A227062 (b = 5), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9), A052224 (b = 10).

Select[Range@ 603, Total@ IntegerDigits[#, 8] == 8 &] (* Michael De Vlieger, Dec 23 2016 *)

select( is(n)=sumdigits(n,8)==8, [1..999]) \\ M. F. Hasler, Dec 23 2016

agen = A226636gen(sod=8, base=8) # generator of terms using code in A226636
print([next(agen) for n in range(1, 55)]) # Michael S. Branicky, Jul 10 2022

[i for i in [0..1000] if sum(Integer(i).digits(base=8))==8]

A227238 Numbers whose base-9 sum of digits is 9.

Original entry on oeis.org

17, 25, 33, 41, 49, 57, 65, 73, 89, 97, 105, 113, 121, 129, 137, 145, 153, 169, 177, 185, 193, 201, 209, 217, 225, 249, 257, 265, 273, 281, 289, 297, 329, 337, 345, 353, 361, 369, 409, 417, 425, 433, 441, 489, 497, 505, 513, 569, 577, 585, 649, 657, 737, 745

Offset: 1

Tom Edgar, Sep 01 2013

All of the entries are odd.
Subsequence of A017077. - Michel Marcus, Sep 02 2013
In general, the set of numbers with sum of base-b digits equal to b is a subset of { (b-1)*k + 1; k = 2, 3, 4, ... }. - M. F. Hasler, Dec 23 2016

			The 9-ary expansion of 17 is (1,8), which has sum of digits 9.
The 9-ary expansion of 169 is (2,0,7), which has sum of digits 9.
10 is not on the list since the 9-ary expansion of 10 is (1,1), which has sum of digits 2 not 9.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A018900, A187813.

Cf. A226636 (b = 3), A226969 (b = 4), A227062 (b = 5), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9), A052224 (b = 10).

Select[Range@ 750, Total@ IntegerDigits[#, 9] == 9 &] (* Michael De Vlieger, Dec 23 2016 *)

select( is(n)=sumdigits(n,9)==9, [1..999]) \\ M. F. Hasler, Dec 23 2016

agen = A226636gen(sod=9, base=9) # generator of terms using code in A226636
print([next(agen) for n in range(1, 55)]) # Michael S. Branicky, Jul 10 2022

[i for i in [0..1000] if sum(Integer(i).digits(base=9))==9]

A048639 Binary encoding of A006881, numbers with two distinct prime divisors.

Original entry on oeis.org

3, 5, 9, 6, 10, 17, 33, 18, 65, 12, 129, 34, 257, 66, 20, 130, 513, 1025, 36, 258, 2049, 24, 4097, 68, 8193, 514, 40, 1026, 16385, 132, 32769, 2050, 260, 65537, 72, 131073, 4098, 8194, 136, 262145, 16386, 524289, 48, 516, 1048577, 1028, 2097153, 32770

Offset: 1

Antti Karttunen, Jul 14 1999

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Permutation of A018900. Cf. A048640, A048623.

encode_A006881 := proc(upto_n) local b,i; b := [ ]; for i from 1 to upto_n do if((0 <> mobius(i)) and (4 = tau(i))) then b := [ op(b), bef(i) ]; fi; od: RETURN(b); end; # see A048623 for bef

Total[2^PrimePi@ # &@ (Map[First, FactorInteger@ #] - 1)] & /@ Select[Range@ 160, SquareFreeQ@ # && PrimeOmega@ # == 2 &] (* Michael De Vlieger, Oct 01 2015 *)

lista(nn) = {for (n=1, nn, if (issquarefree(n) && bigomega(n)==2, f = factor(n); x = sum(k=1, #f~, 2^(primepi(f[k,1])-1)); print1(x, ", ");););} \\ Michel Marcus, Oct 01 2015

from math import isqrt
from sympy import primepi, primerange, primefactors
def A048639(n):
    def f(x): return int(n+x+(t:=primepi(s:=isqrt(x)))+(t*(t-1)>>1)-sum(primepi(x//k) for k in primerange(1, s+1)))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return sum(1<Chai Wah Wu, Feb 22 2025

a(n) = 2^(i-1) + 2^(j-1), where A006881(n) = p_i*p_j (p_i and p_j stand for the i-th and j-th primes respectively, where the first prime is 2).

A066884 Square array read by upward antidiagonals where the n-th row contains the positive integers with n binary 1's.

Original entry on oeis.org

1, 3, 2, 7, 5, 4, 15, 11, 6, 8, 31, 23, 13, 9, 16, 63, 47, 27, 14, 10, 32, 127, 95, 55, 29, 19, 12, 64, 255, 191, 111, 59, 30, 21, 17, 128, 511, 383, 223, 119, 61, 39, 22, 18, 256, 1023, 767, 447, 239, 123, 62, 43, 25, 20, 512, 2047, 1535, 895, 479, 247, 125, 79, 45, 26, 24, 1024

Offset: 1

Jared Benjamin Ricks (jaredricks(AT)yahoo.com), Jan 21 2002

This is a permutation of the positive integers; the inverse permutation is A067587.

			Column: 1   2   3   4   5   6
-----------------------------
Row 1:| 1   2   4   8  16  32
Row 2:| 3   5   6   9  10  12
Row 3:| 7  11  13  14  19  21
Row 4:|15  23  27  29  30  39
Row 5:|31  47  55  59  61  62
Row 6:|63  95 111 119 123 125

Ivan Neretin, Table of n, a(n) for n = 1..8001 (126 antidiagonals)
Vladimir Dobric, M. Skyers, and L. J. Stanley, Polynomial Time Computable Triangular Arrays For Almost Sure Convergence, arXiv preprint arXiv:1603.04896 [math.PR], 2016. [Shows that this sequence is in P-TIME]
Index entries for sequences that are permutations of the natural numbers

Cf. A000120, A067587.
Selected rows: A000079 (1), A018900 (2), A014311 (3), A014312 (4), A014313 (5), A023688 (6), A023689 (7), A023690 (8), A023691 (9), A038461 (10), A038462 (11), A038463 (12). For decimal analogs, see A011557 and A038444-A038452.
Selected columns: A000225 (1), A055010 (2).
Selected diagonals: A036563 (main), A000918 (1st upper), A153894 (2nd upper). [Franklin T. Adams-Watters, Apr 22 2009]
Cf. A067576 (the same array read by downward antidiagonals).
Antidiagonal sums give A361074.

a = {}; Do[ a = Append[a, Last[ Take[ Take[ Select[ Range[2^12], Count[ IntegerDigits[ #, 2], 1] == j - i + 1 & ], j], i]]], {j, 1, 11}, {i, 1, j}]; a

Corrected and extended by Henry Bottomley, Jan 27 2002

A084468 Odd numbers with exactly 3 ones in binary expansion.

Original entry on oeis.org

7, 11, 13, 19, 21, 25, 35, 37, 41, 49, 67, 69, 73, 81, 97, 131, 133, 137, 145, 161, 193, 259, 261, 265, 273, 289, 321, 385, 515, 517, 521, 529, 545, 577, 641, 769, 1027, 1029, 1033, 1041, 1057, 1089, 1153, 1281, 1537, 2051, 2053, 2057, 2065, 2081, 2113, 2177

Offset: 1

Antti Karttunen, Jun 02 2003

Amiram Eldar, Table of n, a(n) for n = 1..10000
Robert Baillie, Summing the curious series of Kempner and Irwin, arXiv:0806.4410 [math.CA], 2008-2015. See p. 18 for Mathematica code irwinSums.m.

Intersection of A005408 and A014311.
A084470(n) gives the position of a(n) in A084467(n).
Cf. A018900.

Flatten[Table[2^m + 2^n + 1, {m, 2, 11}, {n, m - 1}]] (* Alonso del Arte, Jul 08 2011 *)

for(m=2, 9, for(n=1, m-1, print1(2^m+2^n+1", "))) \\ Charles R Greathouse IV, Oct 04 2011

from math import isqrt, comb
def A084468(n): return (1<<(m:=isqrt(n<<3)+1>>1)+1)+(1<<(n-comb(m,2)))|1 # Chai Wah Wu, Apr 07 2025

a(n) = 2*A018900(n) + 1 = A005408(A018900(n)).

Sum_{n>=1} 1/a(n) = 0.714295772926319061998427422200268976390844375453066534198594764887682975019... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022

A140513 Repeat 2^n n times.

Original entry on oeis.org

2, 4, 4, 8, 8, 8, 16, 16, 16, 16, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 128, 128, 128, 128, 128, 128, 128, 256, 256, 256, 256, 256, 256, 256, 256, 512, 512, 512, 512, 512, 512, 512, 512, 512, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024

Offset: 0

Paul Curtz, Jul 01 2008

Reinhard Zumkeller, Rows n = 0..127 of triangle, flattened
Sajed Haque, Chapter 2.6.2 of Discriminators of Integer Sequences, 2017, See p. 34.

Cf. A000079, A018900, A059268, A111650, A137688.

a140513 n k = a140513_tabl !! (n-1) !! (k-1)
a140513_row n = a140513_tabl !! (n-1)
a140513_tabl = iterate (\xs@(x:_) -> map (* 2) (x:xs)) [2]
a140513_list = concat a140513_tabl
-- Reinhard Zumkeller, Nov 14 2015

t={}; Do[r={}; Do[If[k==0||k==n, m=2^n, m=t[[n, k]] + t[[n, k + 1]]]; r=AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t=Flatten[2 t] (* Vincenzo Librandi, Feb 17 2018 *)
Table[Table[2^n,n],{n,10}]//Flatten (* Harvey P. Dale, Dec 04 2018 *)

from math import isqrt
def A140513(n): return 1<<(m:=isqrt(k:=n+1<<1))+(k>m*(m+1)) # Chai Wah Wu, Nov 07 2024

a(n) = 2*A137688(n).
a(n) = A018900(n+1) - A059268(n). - Reinhard Zumkeller, Jun 24 2009
From Reinhard Zumkeller, Feb 28 2010: (Start)
Seen as a triangle read by rows: T(n,k)=2^n, 1 <= k <= n.
T(n,k) = A173786(n-1,k-1) + A173787(n-1,k-1), 1 <= k <= n. (End)
Sum_{n>=0} 1/a(n) = 2. - Amiram Eldar, Aug 16 2022

A239709 Primes of the form m = b^i + b^j - 1, where i > j > 0, b > 1.

Original entry on oeis.org

5, 11, 17, 19, 23, 29, 41, 47, 67, 71, 79, 83, 89, 107, 109, 131, 149, 181, 191, 239, 251, 257, 263, 269, 271, 349, 379, 383, 419, 461, 599, 701, 809, 811, 929, 971, 991, 1009, 1031, 1039, 1087, 1151, 1259, 1279, 1301, 1451, 1481, 1511, 1559, 1721, 1871, 1979, 2063, 2069, 2111, 2161, 2213, 2267, 2351, 2549, 2861, 2939, 2969, 3079, 3191, 3389

Offset: 1

Hieronymus Fischer, Mar 27 2014

nonn

If m is a term, then there is a base b > 1 such that the base-b representation of m has digital sum = 1 + j*(b-1) == 1 (mod (b-1)).
The base b for which m = b^i + b^j - 1 is not uniquely determined. Example: 11 = 2^3+2^2-1 = 3^2 +3^1-1.
Numbers m which satisfy m = b^i + b^j - 1 with odd i and j and b == 2 (mod 3) are not terms. Example: 12189 = 23^3 + 23^1 - 1 is not a prime.

			a(1) = 5, since 5 = 2^2 + 2^1 - 1 is prime.
a(2) = 11, since 11 = 2^3 + 2^2 - 1 is prime.
a(6) = 29, since 29 = 3^3 + 3^1 - 1 is prime.
a(10^1) = 71.
a(10^2) = 13109.
a(10^3) = 9336079.
a(10^4) = 2569932329.
a(10^5) = 455578426189.
a(10^6) = 68543190483641.

Hieronymus Fischer, Table of n, a(n) for n = 1..10000

Cf. A239710, A239711, A239712 - A239720.

Cf. A239708, A018900.

A239709
"Answers the n-th term of A239709.
  Iterative calculation using A239709_termsLTn.
  Usage: n A239709
  Answer: a(n)"
  | n terms m |
  terms := SortedCollection new.
  n := self.
  m := (n prime // 2) squared.
  terms := m A239709_termsLTn.
  [terms size < n] whileTrue:
         [m := 2 * m.
         terms := m A239709_termsLTn].
  ^terms at: n
  "Remark: A last line of
  ^terms copyFrom: 1 to: n
  answers an array of the first n terms"
[by_Hieronymus Fischer_, Apr 14 2014]
-----------

A239709_termsLTn
  "Answers all the terms of A239709 which are < n.
  Direct processing by scanning the scanning the bases b in increasing order, up to b = sqrt(n), and calculating the numbers b^i + b^j - 1.
  Usage: n A239709_termsLTn
  Answer: #(5 11 17 19 23 ...) [terms < n]"
  | bmax p q n m terms a |
  terms := OrderedCollection new.
  n := self.
  bmax := n sqrtTruncated.
  2 to: bmax
     do:
         [:b |
         m := 1 + (n floorLog: b).
         p := b.
         2 to: m
              by: 1
              do:
                   [:i |
                   p := b * p.
                   q := b.
                   1 to: i - 1
                        by: 1
                        do:
                            [:j |
                            a := p + q - 1.
                            a < n ifTrue: [a isPrime ifTrue: [terms add: a]].
                            q := b * q]]].
  ^terms asSet asArray sorted
[by_Hieronymus Fischer_, Apr 14 2014]
-----------

A239709nTerms
  "Alternative version: Answers the first n terms of A239709. Direct calculation by scanning the numbers b^i + b^j - 1 in increasing order.
  Usage: n A239709
  Answer: a(n)"
  | a amax an b bmax k terms p q p_i q_j a_b amin bamin |
  terms := SortedCollection new.
  p_i := OrderedCollection new.
  q_j := OrderedCollection new.
  a_b := OrderedCollection new.
  p_i add: 1.
  q_j add: 1.
  a_b add: 1.
  k := 0.
  b := 2.
  bmax := b.
  p := b * b.
  q := b.
  a := p + q - 1.
  p_i add: p.
  q_j add: q.
  a_b add: a.
  amax := 2 * (b + 1) + a.
  an := 0.
  [(k < self and: [a < amax]) or: [a < an]] whileTrue:
         [[(k < self and: [a < amax]) or: [a < an]] whileTrue:
                   [[q < p and: [(k < self and: [a < amax]) or: [a < an]]] whileTrue:
                            [a isPrime2
                                 ifTrue:
                                      [(terms includes: a)
                                          ifFalse:
                                               [k := k + 1.
                                               terms add: a.
                                               k >= self ifTrue: [an := terms at: self]]].
                            q := b * q.
                            a := p + q - 1].
                   p = q
                        ifTrue:
                            [p := b * p.
                            q := b.
                            a := p + q - 1].
                   p_i at: b put: p.
                   q_j at: b put: q.
                   a_b at: b put: a].
         amin := a.
         2 to: b - 1
              do:
                   [:bb |
                   (a_b at: bb) < amin
                        ifTrue:
                            [amin := a_b at: bb.
                            bamin := bb]].
         b + 1 to: bmax
              do:
                   [:bb |
                   (a_b at: bb) < amin
                        ifTrue:
                            [amin := a_b at: bb.
                            bamin := bb]].
         amin < (a min: amax)
              ifTrue:
                   [b := bamin.
                   p := p_i at: b.
                   q := q_j at: b.
                   a := a_b at: b]
              ifFalse:
                   [bmax := bmax + 1.
                   b := bmax.
                   p := b * b.
                   q := b.
                   a := p + q - 1.
                   p_i add: p.
                   q_j add: q.
                   a_b add: a.
                   amax := 2 * (b + 1) + a max: amax]].
  ^terms copyFrom: 1 to: self
[by_Hieronymus Fischer_, Apr 20 2014]

A357773 Odd numbers with two zeros in their binary expansion.

Original entry on oeis.org

9, 19, 21, 25, 39, 43, 45, 51, 53, 57, 79, 87, 91, 93, 103, 107, 109, 115, 117, 121, 159, 175, 183, 187, 189, 207, 215, 219, 221, 231, 235, 237, 243, 245, 249, 319, 351, 367, 375, 379, 381, 415, 431, 439, 443, 445, 463, 471, 475, 477, 487, 491, 493, 499, 501

Offset: 1

Bernard Schott, Oct 12 2022

A048490 \ {1} is a subsequence, since for m >= 1, A048490(m) = 8*2^m - 7 has 11..11001 with m starting 1 for binary expansion.
A153894 \ {4} is a subsequence, since for m >= 1, A153894(m) = 5*2^m - 1 has 10011..11 with m trailing 1 for binary expansion.
A220236 is a subsequence, since for m >= 1, A220236(m) = 2^(2*m + 2) - 2^(m + 1) - 2^m - 1 has 11..110011..11 with m starting 1 and m trailing 1 for binary expansion.
For k > 2, there are (k-1)*(k-2)/2 terms between 2^k and 2^(k+1), or equivalently (k-1)*(k-2)/2 terms with k+1 bits.
Binary expansion of a(n) is A357774(n).
{4*a(n), n>0} form a subsequence of A353654 (numbers with two trailing 0 bits and two other 0 bits).

Cf. A018900, A005408, A023416, A353654, A357774.
Odd numbers with k zeros in their binary expansion: A000225 (k=0), A190620 (k=1).
Subsequences: A048490 \ {1}, A153894 \ {4}, A220236.

seq(seq(seq(2^n-1-2^i-2^j,j=i-1..1,-1),i=n-2..1,-1),n=4..10); # Robert Israel, Oct 13 2022

Select[Range[1, 500, 2], DigitCount[#, 2, 0] == 2 &] (* Amiram Eldar, Oct 12 2022 *)

isok(k) = (k%2) && (#binary(k) == hammingweight(k)+2); \\ Michel Marcus, Oct 13 2022

list(lim)=my(v=List()); for(n=4,logint(lim\=1,2)+1, my(N=2^n-1); forstep(a=n-2,2,-1, my(A=N-1<lim, break(2)); listput(v,t)))); Vec(v) \\ Charles R Greathouse IV, Oct 21 2022

def a(n):
    m = 0
    while m*(m+1)*(m+2)//6 <= n: m += 1
    m -= 1 # m = A056556(n-1)
    k, r, j = m + 4, n - m*(m+1)*(m+2)//6, 0
    while r >= 0: r -= (m+1-j); j += 1
    j += 1
    return 2**k - 2**(k-j) - 2**(-r) - 1
print([a(n) for n in range(60)]) # Michael S. Branicky, Oct 12 2022

# faster version for generating initial segment of sequence
from itertools import combinations, count, islice
def agen():
    for d in count(4):
        b, c = 2**d - 1, 2**(d-1)
        for i, j in combinations(range(1, d-1), 2):
            yield b - (c >> i) - (c >> j)
print(list(islice(agen(), 60))) # Michael S. Branicky, Oct 13 2022

from math import comb, isqrt
from sympy import integer_nthroot
def A357773(n):
    a = (m:=integer_nthroot(6*n, 3)[0])+(n>comb(m+2,3))+3
    b = isqrt((j:=comb(a-1,3)-n+1)<<3)+3>>1
    c = j-comb((r:=isqrt(w:=j<<1))+(w>r*(r+1)),2)
    return (1<Chai Wah Wu, Dec 17 2024

A023416(a(n)) = 2.

a((n-1)*(n-2)*(n-3)/6 - (i-1)*(i-2)/2 - (j-1)) = 2^n - 2^i - 2^j - 1 for 1 <= j < i <= n-2. - Robert Israel, Oct 13 2022

a(11) and beyond from Michael S. Branicky, Oct 12 2022

A087323 a(n) = (n+1) * 2^n - 1.

Original entry on oeis.org

0, 3, 11, 31, 79, 191, 447, 1023, 2303, 5119, 11263, 24575, 53247, 114687, 245759, 524287, 1114111, 2359295, 4980735, 10485759, 22020095, 46137343, 96468991, 201326591, 419430399, 872415231, 1811939327, 3758096383, 7784628223, 16106127359, 33285996543, 68719476735

Offset: 0

Amarnath Murthy, Sep 03 2003

Row sums of triangle in A018900 (without the initial 0). - Reinhard Zumkeller, Jun 24 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..3000 (corrected by Ray Chandler, Jan 19 2019)
Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Cf. A087322 (a triangle which includes this sequence as the leading diagonal but without the initial zero).

[((n+1)*2^n - 1): n in [1..30]]; // Vincenzo Librandi, Sep 29 2011

Table[(n + 1)2^n - 1, {n, 0, 29}] (* Alonso del Arte, Jan 31 2014 *)
LinearRecurrence[{5,-8,4},{0,3,11},40] (* Harvey P. Dale, Sep 15 2019 *)

a(n) = (n + 1) * 2^n - 1 = 2^n * n + 2^n - 1.
a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). G.f.: x*(3-4*x)/((1-x)*(1-2*x)^2). - Colin Barker, Mar 23 2012
a(n) = A001787(n+1) - 1. - Omar E. Pol, Nov 09 2013

Edited and extended by David Wasserman, May 06 2005

Formula promoted to definition and offset adjusted to 0 by Alonso del Arte, Jan 31 2014

cp's OEIS Frontend

A227092 Numbers whose base-7 sum of digits is 7.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Sage

A227095 Numbers whose base-8 sum of digits is 8.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Sage

A227238 Numbers whose base-9 sum of digits is 9.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Sage

A048639 Binary encoding of A006881, numbers with two distinct prime divisors.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula

A066884 Square array read by upward antidiagonals where the n-th row contains the positive integers with n binary 1's.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A084468 Odd numbers with exactly 3 ones in binary expansion.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A140513 Repeat 2^n n times.

Views

Author

Keywords

Links

Crossrefs