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

0, 1001, 10010, 10101, 11011, 100100, 101010, 101101, 110110, 111111, 1000111, 1001000, 1010100, 1011010, 1011101, 1100001, 1101100, 1110011, 1111110, 10000011, 10001110, 10010000, 10011001, 10100111, 10101000, 10110100, 10111010, 10111101, 11000010, 11000101, 11001011, 11010111, 11011000

Offset: 1

Author

Robert Israel, Oct 31 2019

Keywords

• nonn
• base

Comments

If x and y are members of the sequence and 10^k > y, then 10^k*x+y is a member.

The number of terms of up to k digits is A263366(k-1).

Examples

			a(3)=10010 is in the sequence because it is divisible by 7 and each of its decimal digits is 0 or 1.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Mathematics StackExchange, Divisibility by 7 of a number consisting of 0 and 1s

Crossrefs

Intersection of A007088 and A008589.

Cf. A263366.

Programs

Magma

a:=[]; f:=func; 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

Maple

bintodec:= proc(n) local L,i; L:= convert(n,base,2); add(10^(i-1)*L[i],i=1..nops(L)) end proc:
select(t -> t mod 7 = 0, map(bintodec,[$0..1000]));

Python

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