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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). 1
1, 2, 3, 7, 10, 20, 27, 31, 40, 127, 138, 219, 245, 276, 552, 650, 682, 1364, 2047, 2728, 8191, 10922, 13515, 14043, 32747, 112347, 131071, 524287, 2796202, 3459945, 5592404, 7124187, 8388607, 8530050, 10660010, 11184808, 16645111, 17060100, 21320020, 33554431 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
In other words, the ones in the binary representation of a term of this sequence encode the first numbers coprime to this term.
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.
See A320673 for similar sequences.
LINKS
EXAMPLE
The first terms, alongside their binary representation and the coprime numbers encoded therein, are:
n a(n) bin(a(n)) First numbers coprime
-- ---- --------- ---------------------
1 1 1 1
2 2 10 1
3 3 11 1, 2
4 7 111 1, 2, 3
5 10 1010 1, 3
6 20 10100 1, 3
7 27 11011 1, 2, 4, 5
8 31 11111 1, 2, 3, 4, 5
9 40 101000 1, 3
10 127 1111111 1, 2, 3, 4, 5, 6, 7
PROG
(PARI) is(n) = my (b=binary(n)); b==vector(#b, k, gcd(n, k)==1)
CROSSREFS
Sequence in context: A356364 A173132 A351704 * A336414 A095010 A295723
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Oct 19 2018
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)