cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 17 results. Next

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

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A011557, A157711 (primes subsequence).
Cf. A038444, A038445, A038447, A038448, A038449, A038450, A038451, A038452, A038453, A038454.

Programs

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

Extensions

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

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A011557.
Cf. A038444, A038445, A038446, A038447, A038448, A038449, A038450, A038451, A038453, A038454.

Programs

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

Extensions

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

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A011557.
Cf. A038444, A038445, A038446, A038447, A038449, A038450, A038451, A038452, A038453, A038454.

Programs

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

Extensions

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

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A011557.
Cf. A038444, A038445, A038446, A038447, A038448, A038450, A038451, A038452, A038453, A038454.

Programs

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

Extensions

Offset corrected by Amiram Eldar, Jul 12 2022

A038453 Sums of 11 distinct powers of 10.

Original entry on oeis.org

11111111111, 101111111111, 110111111111, 111011111111, 111101111111, 111110111111, 111111011111, 111111101111, 111111110111, 111111111011, 111111111101, 111111111110, 1001111111111, 1010111111111, 1011011111111, 1011101111111, 1011110111111, 1011111011111, 1011111101111
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A011557.
Cf. A038444, A038445, A038446, A038447, A038448, A038449, A038450, A038451, A038452, A038454.

Programs

  • Mathematica
    Union[Total/@Subsets[10^Range[0,12],{11}]] (* Harvey P. Dale, Jan 20 2013 *)
  • PARI
    lista(nn) = {for (n=1, nn, if (hammingweight(n) == 11, print1(subst(Pol(binary(n)), x, 10), ", ");););} \\ Michel Marcus, Feb 29 2016
  • Python
    from itertools import islice
def A038453_gen(): # generator of terms
    yield int(bin(n:=2047)[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:])
A038453_list = list(islice(A038453_gen(),20)) # Chai Wah Wu, Mar 11 2025

Extensions

Offset changed to 1 by Ivan Neretin, Feb 28 2016

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

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A011557.
Cf. A038444, A038445, A038446, A038447, A038448, A038449, A038450, A038451, A038452, A038453.

Programs

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

Formula

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

Extensions

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

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A011557.
Cf. A038444, A038445, A038446, A038447, A038448, A038449, A038451, A038452, A038453, A038454.

Programs

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

Extensions

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

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A011557.
Cf. A038444, A038445, A038446, A038447, A038448, A038449, A038450, A038452, A038453, A038454.

Programs

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

Extensions

Offset corrected by Amiram Eldar, Jul 12 2022

A038465 Sums of 3 distinct powers of 3.

Original entry on oeis.org

13, 31, 37, 39, 85, 91, 93, 109, 111, 117, 247, 253, 255, 271, 273, 279, 325, 327, 333, 351, 733, 739, 741, 757, 759, 765, 811, 813, 819, 837, 973, 975, 981, 999, 1053, 2191, 2197, 2199, 2215, 2217, 2223, 2269, 2271, 2277, 2295, 2431, 2433, 2439, 2457, 2511, 2917
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Base 3 interpretation of A038445.
Cf. A000244, A038464, A038466, A038467, A038468, A038469.

Programs

  • Mathematica
    Total/@Subsets[3^Range[0,10],{3}]//Union (* Harvey P. Dale, Jul 10 2017 *)
  • Python
    from math import comb, isqrt
from sympy import integer_nthroot
def A038465(n): return 3**((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))+3**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+3**(m+t+1) # Chai Wah Wu, Apr 04 2025

Extensions

Offset corrected by Amiram Eldar, Jul 13 2022

A038471 Sums of 3 distinct powers of 4.

Original entry on oeis.org

21, 69, 81, 84, 261, 273, 276, 321, 324, 336, 1029, 1041, 1044, 1089, 1092, 1104, 1281, 1284, 1296, 1344, 4101, 4113, 4116, 4161, 4164, 4176, 4353, 4356, 4368, 4416, 5121, 5124, 5136, 5184, 5376, 16389, 16401, 16404, 16449, 16452, 16464, 16641, 16644, 16656, 16704
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Base 4 interpretation of A038445.
Cf. A000302, A038470, A038472, A038473.

Programs

  • Mathematica
    Union[Total/@Subsets[4^Range[0,10],{3}]] (* Harvey P. Dale, Oct 20 2012 *)
  • Python
    from math import isqrt, comb
from sympy import integer_nthroot
def A038471(n): return (1<<((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)<<1))+(1<<((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1)<<1))+(1<<(m+t+1<<1)) # Chai Wah Wu, Apr 04 2025

Extensions

Offset corrected by Amiram Eldar, Jul 13 2022
Showing 1-10 of 17 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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