A038454 Sums of 12 distinct powers of 10.

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

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

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

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