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A280998
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Numbers with a prime number of 1's in their binary reflected Gray code representation.
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5
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2, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 19, 21, 23, 24, 25, 27, 28, 29, 30, 32, 33, 35, 37, 39, 41, 43, 45, 47, 48, 49, 51, 53, 55, 56, 57, 59, 60, 61, 62, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 96, 97, 99, 101, 103
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internal format)
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OFFSET
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1,1
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COMMENTS
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From Emeric Deutsch, Jan 28 2018: (Start) Also the indices of the compositions that have a prime number of parts. For the definition of the index of a composition see _A298644_. For example, 27 is in the sequence since its binary form is 11011 and the composition [2,1,2] has 3 parts. On the other hand,58 is not in the sequence since its binary form is 111010 and the composition [3,1,1,1] has 4 parts. The command c(n) from the Maple program yields the composition having index n. (End)
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LINKS
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Indranil Ghosh, Table of n, a(n) for n = 1..10001
Wikipedia, Gray code.
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EXAMPLE
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27 is in the sequence because the binary reflected Gray code representation of 27 is 10110 which has 3 1's, and 3 is prime.
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MAPLE
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Runs := proc (L) local j, r, i, k: j := 1: r[j] := L[1]: for i from 2 to nops(L) do if L[i] = L[i-1] then r[j] := r[j], L[i] else j := j+1: r[j] := L[i] end if end do: [seq([r[k]], k = 1 .. j)] end proc: RunLengths := proc (L) map(nops, Runs(L)) end proc: c := proc (n) ListTools:-Reverse(convert(n, base, 2)): RunLengths(%) end proc: A := {}: for n to 175 do if isprime(nops(c(n))) = true then A := `union`(A, {n}) else end if end do: A; # most of the Maple program is due to W. Edwin Clark. # Emeric Deutsch, Jan 28 2018
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MATHEMATICA
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Select[Range[100], PrimeQ[DigitCount[BitXor[#, Floor[#/2]], 2, 1]] &] (* Amiram Eldar, May 01 2021 *)
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PROG
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(PARI) is(n)=isprime(hammingweight(bitxor(n, n>>1))) \\ Charles R Greathouse IV, Jan 12 2017
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CROSSREFS
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Cf. A014550, A052294, A005811, A298644, A101211.
Sequence in context: A328594 A346129 A288174 * A043687 A087118 A249115
Adjacent sequences: A280995 A280996 A280997 * A280999 A281000 A281001
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KEYWORD
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nonn,base,easy
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AUTHOR
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Indranil Ghosh, Jan 12 2017
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STATUS
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approved
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