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A320675
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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).
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1
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
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PROG
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(PARI) is(n) = my (b=binary(n)); b==vector(#b, k, gcd(n, k)==1)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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