A038453 -id:A038453 - cp's OEIS frontend

A038445 Sums of 3 distinct powers of 10.

111, 1011, 1101, 1110, 10011, 10101, 10110, 11001, 11010, 11100, 100011, 100101, 100110, 101001, 101010, 101100, 110001, 110010, 110100, 111000, 1000011, 1000101, 1000110, 1001001, 1001010, 1001100, 1010001, 1010010, 1010100, 1011000, 1100001, 1100010, 1100100

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A011557.

Cf. A038444, A038446, A038447, A038448, A038449, A038450, A038451, A038452, A038453, A038454.

Sort[Plus @@@ Subsets[10^Range[0, 6], {3}]] (* Amiram Eldar, Jul 12 2022 *)

from math import isqrt, comb
from sympy import integer_nthroot
def A038445(n): return 10**((r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+10**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+10**(m+t+1) # Chai Wah Wu, Mar 10 2025

A038446 Sums of 4 distinct powers of 10.

Original entry on oeis.org

1111, 10111, 11011, 11101, 11110, 100111, 101011, 101101, 101110, 110011, 110101, 110110, 111001, 111010, 111100, 1000111, 1001011, 1001101, 1001110, 1010011, 1010101, 1010110, 1011001, 1011010, 1011100, 1100011, 1100101, 1100110, 1101001, 1101010, 1101100, 1110001

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A011557, A157711 (primes subsequence).

Cf. A038444, A038445, A038447, A038448, A038449, A038450, A038451, A038452, A038453, A038454.

Total/@Subsets[10^Range[0,6],{4}]//Union (* Harvey P. Dale, Nov 07 2021 *)

from itertools import islice
def A038446_gen(): # generator of terms
    yield int(bin(n:=15)[2:])
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:])
A038446_list = list(islice(A038446_gen(),20)) # Chai Wah Wu, Mar 11 2025

Offset corrected by Amiram Eldar, Jul 12 2022

A038452 Sums of 10 distinct powers of 10.

Original entry on oeis.org

1111111111, 10111111111, 11011111111, 11101111111, 11110111111, 11111011111, 11111101111, 11111110111, 11111111011, 11111111101, 11111111110, 100111111111, 101011111111, 101101111111, 101110111111, 101111011111, 101111101111, 101111110111, 101111111011, 101111111101

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A011557.

Cf. A038444, A038445, A038446, A038447, A038448, A038449, A038450, A038451, A038453, A038454.

Take[Union[Total/@Subsets[10^Range[0,15],{10}]],20] (* Harvey P. Dale, Dec 19 2011 *)

from itertools import islice
def A038452_gen(): # generator of terms
    yield int(bin(n:=1023)[2:])
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:])
A038452_list = list(islice(A038452_gen(),20)) # Chai Wah Wu, Mar 10 2025

Offset changed to 1 by Ivan Neretin, Feb 28 2016

A038448 Sums of 6 distinct powers of 10.

Original entry on oeis.org

111111, 1011111, 1101111, 1110111, 1111011, 1111101, 1111110, 10011111, 10101111, 10110111, 10111011, 10111101, 10111110, 11001111, 11010111, 11011011, 11011101, 11011110, 11100111, 11101011, 11101101, 11101110, 11110011, 11110101, 11110110, 11111001, 11111010

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A011557.

Cf. A038444, A038445, A038446, A038447, A038449, A038450, A038451, A038452, A038453, A038454.

Sort[Plus @@@ Subsets[10^Range[0, 7], {6}]] (* Amiram Eldar, Jul 12 2022 *)

from itertools import islice
def A038448_gen(): # generator of terms
    yield int(bin(n:=63)[2:])
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:])
A038448_list = list(islice(A038448_gen(),20)) # Chai Wah Wu, Mar 11 2025

Offset corrected by Amiram Eldar, Jul 12 2022

A038449 Sums of 7 distinct powers of 10.

Original entry on oeis.org

1111111, 10111111, 11011111, 11101111, 11110111, 11111011, 11111101, 11111110, 100111111, 101011111, 101101111, 101110111, 101111011, 101111101, 101111110, 110011111, 110101111, 110110111, 110111011, 110111101, 110111110, 111001111, 111010111, 111011011, 111011101

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A011557.

Cf. A038444, A038445, A038446, A038447, A038448, A038450, A038451, A038452, A038453, A038454.

Take[Total/@Subsets[10^Range[0,20],{7}]//Union,20] (* Harvey P. Dale, Feb 25 2018 *)

from itertools import islice
def A038449_gen(): # generator of terms
    yield int(bin(n:=127)[2:])
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:])
A038449_list = list(islice(A038449_gen(),20)) # Chai Wah Wu, Mar 11 2025

Offset corrected by Amiram Eldar, Jul 12 2022

A038454 Sums of 12 distinct powers of 10.

Original entry on oeis.org

111111111111, 1011111111111, 1101111111111, 1110111111111, 1111011111111, 1111101111111, 1111110111111, 1111111011111, 1111111101111, 1111111110111, 1111111111011, 1111111111101, 1111111111110, 10011111111111, 10101111111111, 10110111111111, 10111011111111, 10111101111111

Offset: 1

Olivier Gérard

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A011557.

Cf. A038444, A038445, A038446, A038447, A038448, A038449, A038450, A038451, A038452, A038453.

N:= 14: # to get all terms of at most N digits
sort(map(t -> (10^N-1)/9 - add(10^j, j=t),
combinat:-choose([$0..N-1],N-12))); # Robert Israel, Feb 28 2016

Sort[Plus @@@ Subsets[10^Range[0, 12], {12}]] (* Amiram Eldar, Jul 12 2022 *)

from itertools import islice
def A038454_gen(): # generator of terms
    yield int(bin(n:=4095)[2:])
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:])
A038454_list = list(islice(A038454_gen(),20)) # Chai Wah Wu, Mar 11 2025

a(binomial(N,12)+k) = 10^N + A038453(k) for 1 <= k <= binomial(N,11). - Robert Israel, Feb 28 2016

Offset changed to 1 by Ivan Neretin, Feb 28 2016

A038450 Sums of 8 distinct powers of 10.

Original entry on oeis.org

11111111, 101111111, 110111111, 111011111, 111101111, 111110111, 111111011, 111111101, 111111110, 1001111111, 1010111111, 1011011111, 1011101111, 1011110111, 1011111011, 1011111101, 1011111110, 1100111111, 1101011111, 1101101111, 1101110111, 1101111011, 1101111101

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A011557.

Cf. A038444, A038445, A038446, A038447, A038448, A038449, A038451, A038452, A038453, A038454.

Sort[FromDigits/@Permutations[{1,1,1,1,1,1,1,1,0,0}]] (* Harvey P. Dale, Apr 29 2013 *)

from itertools import islice
def A038450_gen(): # generator of terms
    yield int(bin(n:=255)[2:])
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:])
A038450_list = list(islice(A038450_gen(),20)) # Chai Wah Wu, Mar 11 2025

Offset corrected by Amiram Eldar, Jul 12 2022

A038451 Sums of 9 distinct powers of 10.

Original entry on oeis.org

111111111, 1011111111, 1101111111, 1110111111, 1111011111, 1111101111, 1111110111, 1111111011, 1111111101, 1111111110, 10011111111, 10101111111, 10110111111, 10111011111, 10111101111, 10111110111, 10111111011

Offset: 1

Olivier Gérard

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A011557.

Cf. A038444, A038445, A038446, A038447, A038448, A038449, A038450, A038452, A038453, A038454.

Sort[Plus @@@ Subsets[10^Range[0, 10], {9}]] (* Amiram Eldar, Jul 12 2022 *)

from itertools import islice
def A038451_gen(): # generator of terms
    yield int(bin(n:=511)[2:])
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:])
A038451_list = list(islice(A038451_gen(),20)) # Chai Wah Wu, Mar 11 2025

Offset corrected by Amiram Eldar, Jul 12 2022

A038462 Sums of 11 distinct powers of 2.

Original entry on oeis.org

2047, 3071, 3583, 3839, 3967, 4031, 4063, 4079, 4087, 4091, 4093, 4094, 5119, 5631, 5887, 6015, 6079, 6111, 6127, 6135, 6139, 6141, 6142, 6655, 6911, 7039, 7103, 7135, 7151, 7159, 7163, 7165, 7166, 7423, 7551, 7615, 7647, 7663, 7671

Offset: 1

Olivier Gérard

Ivan Neretin, 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.

Base 2 interpretation of A038453.

Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691, A038461 (Hamming weight = 1, 2, ..., 10).

Select[Range[8000], DigitCount[#, 2, 1] == 11 &] (* Amiram Eldar, Feb 14 2022 *)

from itertools import islice
def A038462_gen(): # generator of terms
    yield (n:=2047)
    while True: yield (n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b)
A038462_list = list(islice(A038462_gen(),20)) # Chai Wah Wu, Mar 10 2025

Sum_{n>=1} 1/a(n) = 1.386300330514503033229968047555778179200262625510401687087371496738972082061... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022

Offset changed to 1 by Ivan Neretin, Feb 28 2016

cp's OEIS Frontend

A038445 Sums of 3 distinct powers of 10.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

A038446 Sums of 4 distinct powers of 10.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

Extensions

A038452 Sums of 10 distinct powers of 10.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

Extensions

A038448 Sums of 6 distinct powers of 10.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

Extensions

A038449 Sums of 7 distinct powers of 10.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

Extensions

A038454 Sums of 12 distinct powers of 10.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Python

Formula

Extensions

A038450 Sums of 8 distinct powers of 10.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

Extensions

A038451 Sums of 9 distinct powers of 10.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica