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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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified April 7 11:07 EDT 2020. Contains 333301 sequences. (Running on oeis4.)