

A328947


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


1



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
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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(k1).


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^(i1)*L[i], i=1..nops(L)) end proc:
select(t > t mod 7 = 0, map(bintodec, [$0..1000]));


PROG

(MAGMA) a:=[]; f:=func<nSeqint(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: A259080 A100709 A130600 * A114387 A204965 A192776
Adjacent sequences: A328944 A328945 A328946 * A328948 A328949 A328950


KEYWORD

nonn,base


AUTHOR

Robert Israel, Oct 31 2019


STATUS

approved



