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A320674
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Positive integers m with binary expansion (b_1, ..., b_k) (where k = A070939(m)) such that b_i = [m == 0 (mod prime(i))] for i = 1..k (where prime(i) denotes the i-th prime number and [] is an Iverson bracket).
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2
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2, 4, 6, 8, 10, 12, 16, 20, 24, 32, 40, 48, 64, 80, 96, 128, 160, 192, 256, 320, 384, 512, 640, 768, 1024, 1280, 1536, 2048, 2560, 3072, 4096, 5120, 6144, 8192, 10240, 12288, 16384, 20480, 24576, 32768, 40960, 49152, 65536, 81920, 98304, 131072, 163840, 196608
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OFFSET
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1,1
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COMMENTS
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In other words, the 1's in the binary representation of a term of this sequence encode the first prime divisors of this term.
All terms are even.
All even terms in A029747 belong to this sequence.
The term a(71) = 33554434 is the first one that does not belong to A029747.
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LINKS
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EXAMPLE
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The initial terms, alongside their binary representation and the prime divisors encoded therein, are:
n a(n) bin(a(n)) First prime divisors
-- -------- -------------------------- --------------------
1 2 10 2
2 4 100 2
3 6 110 2, 3
4 8 1000 2
5 10 1010 2, 5
6 12 1100 2, 3
7 16 10000 2
8 20 10100 2, 5
9 24 11000 2, 3
...
71 33554434 10000000000000000000000010 2, 97
...
33554434 is in the sequence because its binary expansion 10000000000000000000000010 of length 26 has a 1 in the 1st place and in the 25th place from the left and 0 elsewhere. As it is divisible by the 1st and 25th prime and by no other prime with index <= 26, 33554434 in the sequence. - David A. Corneth, Oct 20 2018
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MATHEMATICA
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selQ[n_] := With[{bb = IntegerDigits[n, 2]}, (Prime /@ Flatten[Position[bb, 1]]) == FactorInteger[n][[All, 1]]];
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PROG
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(PARI) is(n) = my (b=binary(n)); b==vector(#b, k, n%prime(k)==0)
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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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