cp's OEIS Frontend

A320675 Positive integers m with binary expansion (b_1, ..., b_k) (where k = A070939(m)) such that b_i = [gcd(m, i)=1] for i = 1..k (where [] is an Iverson bracket).

%I A320675 #12 Oct 24 2018 12:01:49
%S A320675 1,2,3,7,10,20,27,31,40,127,138,219,245,276,552,650,682,1364,2047,
%T A320675 2728,8191,10922,13515,14043,32747,112347,131071,524287,2796202,
%U A320675 3459945,5592404,7124187,8388607,8530050,10660010,11184808,16645111,17060100,21320020,33554431
%N A320675 Positive integers m with binary expansion (b_1, ..., b_k) (where k = A070939(m)) such that b_i = [gcd(m, i)=1] for i = 1..k (where [] is an Iverson bracket).
%C A320675 In other words, the ones in the binary representation of a term of this sequence encode the first numbers coprime to this term.
%C A320675 This sequence contains every term of A001348: 2^2 - 1 belongs to this sequence, and for any odd prime number p, if q divides 2^p - 1, then q > p and gcd(p, i) = 1 for i = 1..p.
%C A320675 See A320673 for similar sequences.
%e A320675 The first terms, alongside their binary representation and the coprime numbers encoded therein, are:
%e A320675   n   a(n)  bin(a(n))  First numbers coprime
%e A320675   --  ----  ---------  ---------------------
%e A320675    1     1  1          1
%e A320675    2     2  10         1
%e A320675    3     3  11         1, 2
%e A320675    4     7  111        1, 2, 3
%e A320675    5    10  1010       1, 3
%e A320675    6    20  10100      1, 3
%e A320675    7    27  11011      1, 2, 4, 5
%e A320675    8    31  11111      1, 2, 3, 4, 5
%e A320675    9    40  101000     1, 3
%e A320675   10   127  1111111    1, 2, 3, 4, 5, 6, 7
%o A320675 (PARI) is(n) = my (b=binary(n)); b==vector(#b, k, gcd(n, k)==1)
%Y A320675 Cf. A001348, A070939, A320673.
%K A320675 nonn,base
%O A320675 1,2
%A A320675 _Rémy Sigrist_, Oct 19 2018