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

1,2

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).

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

Example

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

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]));

Prog

(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
(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

Crossrefs

Intersection of A007088 and A008589.

Cf. A263366.

Sequence in context: A100709 A372419 A130600 * A114387 A357774 A204965

Adjacent sequences: A328944 A328945 A328946 * A328948 A328949 A328950

Keyword

nonn,base

Author

Robert Israel, Oct 31 2019

Status

approved