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A328947 Numbers formed from decimal digits 0 and/or 1 which are divisible by 7.

%I A328947 #20 Sep 08 2022 08:46:24
%S A328947 0,1001,10010,10101,11011,100100,101010,101101,110110,111111,1000111,
%T A328947 1001000,1010100,1011010,1011101,1100001,1101100,1110011,1111110,
%U A328947 10000011,10001110,10010000,10011001,10100111,10101000,10110100,10111010,10111101,11000010,11000101,11001011,11010111,11011000
%N A328947 Numbers formed from decimal digits 0 and/or 1 which are divisible by 7.
%C A328947 If x and y are members of the sequence and 10^k > y, then 10^k*x+y is a member.
%C A328947 The number of terms of up to k digits is A263366(k-1).
%H A328947 Chai Wah Wu, <a href="/A328947/b328947.txt">Table of n, a(n) for n = 1..10000</a>
%H A328947 Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/3417330/divisibility-by-7-of-a-number-consisting-of-0-and-1s#3417339">Divisibility by 7 of a number consisting of 0 and 1s</a>
%e A328947 a(3)=10010 is in the sequence because it is divisible by 7 and each of its decimal digits is 0 or 1.
%p A328947 bintodec:= proc(n) local L,i; L:= convert(n,base,2); add(10^(i-1)*L[i],i=1..nops(L)) end proc:
%p A328947 select(t -> t mod 7 = 0, map(bintodec,[$0..1000]));
%o A328947 (Magma) a:=[]; f:=func<n|Seqint(Intseq(Seqint(Intseq(n),10),2))>; for k in [0..220] do if f(k) mod 7 eq 0 then Append(~a,f(k)); end if; end for; a; // _Marius A. Burtea_, Nov 01 2019
%o A328947 (Python)
%o A328947 A328947_list = [n for n in (int(bin(m)[2:]) for m in range(10**4)) if not n % 7] # _Chai Wah Wu_, Nov 01 2019
%Y A328947 Intersection of A007088 and A008589.
%Y A328947 Cf. A263366.
%K A328947 nonn,base
%O A328947 1,2
%A A328947 _Robert Israel_, Oct 31 2019