A038446 -id:A038446 - 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

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

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

Olivier Gérard

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

Cf. A011557.

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

Union[Total/@Subsets[10^Range[0,12],{11}]] (* Harvey P. Dale, Jan 20 2013 *)

lista(nn) = {for (n=1, nn, if (hammingweight(n) == 11, print1(subst(Pol(binary(n)), x, 10), ", ");););} \\ Michel Marcus, Feb 29 2016

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

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

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

A157711 Primes made up of 0's and four 1's only.

Original entry on oeis.org

10111, 1011001, 1100101, 10010101, 10100011, 101001001, 1000001011, 1000010101, 1010000011, 1100010001, 10000001101, 10001000011, 10001001001, 10001100001, 10100000011, 10100001001, 11000000101, 11001000001

Offset: 1

Lekraj Beedassy, Mar 04 2009

Intersection of A062339 and A020449. Subsequence of A235154. - Felix Fröhlich, Nov 19 2014

Primes that are the sum of four distinct powers of ten (A038446). - Jeppe Stig Nielsen, May 18 2023

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
Hans Havermann, The one-millionth term.
Hans Havermann, The two-millionth term.

Cf. A020449, A038446, A062339, A235154, A383675 (number of n-digit terms).

for d from 4 to 18 do for c from 0 to 2^d-1 do bdgs := convert(c,base,2) ; if add(i,i=bdgs) = 3 then p := 10^d+add(op(i,bdgs)*10^(i-1),i=1..nops(bdgs)) ; if isprime(p) then printf("%d,",p) ; fi; fi; od: od: # R. J. Mathar, Mar 06 2009

Flatten[Select[FromDigits/@Permutations[Join[{1,1,1,1},PadRight[{},7,0]]],PrimeQ]] // Union (* Harvey P. Dale, May 09 2019 *)

for(n=0, 10, forprime(p=10^n, (10^(n+1)-1)/9, if(vecmax(digits(p))==1, if(sumdigits(p)==4, print1(p, ", "))))) \\ Felix Fröhlich, Nov 19 2014

my(M=20);for(i=3, M, for(j=2,i-1, for(k=1, j-1, my(p=10^i+10^j+10^k+1); isprime(p)&&print1(p,", ")))) \\ Jeppe Stig Nielsen, May 18 2023

Extended by numerous authors, Mar 06 2009

A038466 Sums of 4 distinct powers of 3.

Original entry on oeis.org

40, 94, 112, 118, 120, 256, 274, 280, 282, 328, 334, 336, 352, 354, 360, 742, 760, 766, 768, 814, 820, 822, 838, 840, 846, 976, 982, 984, 1000, 1002, 1008, 1054, 1056, 1062, 1080, 2200, 2218, 2224, 2226, 2272, 2278, 2280, 2296, 2298, 2304, 2434, 2440, 2442, 2458

Offset: 1

Olivier Gérard

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

Base 3 interpretation of A038446.

Cf. A000244, A038464, A038465, A038467, A038468, A038469.

Sort[Plus @@@ Subsets[3^Range[0, 7], {4}]] (* Amiram Eldar, Jul 13 2022 *)

from itertools import islice
def A038466_gen(): # generator of terms
    yield int(bin(n:=15)[2:],3)
    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:],3)
A038466_list = list(islice(A038466_gen(),30)) # Chai Wah Wu, Apr 04 2025

Offset corrected by Amiram Eldar, Jul 13 2022

cp's OEIS Frontend

A038445 Sums of 3 distinct powers of 10.

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A038452 Sums of 10 distinct powers of 10.

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A038448 Sums of 6 distinct powers of 10.

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A038449 Sums of 7 distinct powers of 10.

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A038453 Sums of 11 distinct powers of 10.

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A038454 Sums of 12 distinct powers of 10.

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A038450 Sums of 8 distinct powers of 10.

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A038451 Sums of 9 distinct powers of 10.

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