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A303077
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a(1) = 1, and for n > 1, a(n) is the greatest prime number whose binary digits appear in order but not necessarily as consecutive digits in the binary representation of n.
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2
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1, 2, 3, 2, 5, 3, 7, 2, 5, 5, 11, 3, 13, 7, 7, 2, 17, 5, 19, 5, 13, 11, 23, 3, 13, 13, 13, 7, 29, 7, 31, 2, 17, 17, 19, 5, 37, 19, 23, 5, 41, 13, 43, 11, 29, 23, 47, 3, 17, 13, 19, 13, 53, 13, 31, 7, 29, 29, 59, 7, 61, 31, 31, 2, 17, 17, 67, 17, 37, 19, 71, 5
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OFFSET
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1,2
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COMMENTS
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This sequence has similarities with A078833; there binary digits have to be consecutive, here not.
For n > 1, a(n) is the greatest prime number appearing in the n-th row of A301983.
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LINKS
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FORMULA
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a(2*n) = a(n) for any n > 1.
a(n) = n iff n is not composite.
a(n) = 2 iff n = 2^k for some k > 0.
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EXAMPLE
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The first terms, alongside the binary representations of n and of a(n), are:
n a(n) bin(n) bin(a(n))
-- ---- ------ ---------
1 1 1 1
2 2 10 10
3 3 11 11
4 2 100 10_
5 5 101 101
6 3 110 11_
7 7 111 111
8 2 1000 10__
9 5 1001 10_1
10 5 1010 101_
11 11 1011 1011
12 3 1100 11__
13 13 1101 1101
14 7 1110 111_
15 7 1111 111_
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PROG
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(PARI) a(n) = my (s=Set(1), b=binary(n)); for (i=2, #b, s=setunion(s, Set(apply(k->2*k+b[i], s)))); vecmax(select(k->k==1 || isprime(k), s))
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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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