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A159006
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Transformation of prime(n): flip digits in the binary representation, revert the sequence of digits, and convert back to decimal.
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1
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2, 0, 2, 0, 2, 4, 14, 6, 2, 8, 0, 22, 26, 10, 2, 20, 8, 16, 30, 14, 54, 6, 26, 50, 60, 44, 12, 20, 36, 56, 0, 62, 110, 46, 86, 22, 70, 58, 26, 74, 50, 82, 2, 124, 92, 28, 52, 4, 56, 88, 104, 8, 112, 32, 254, 62, 158, 30, 174, 206, 78, 182, 102, 38, 198, 134, 90, 234, 74, 138, 242
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OFFSET
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1,1
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COMMENTS
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Write the n-th prime in binary as in A004676. Change all 0's to 1's and all 1's to 0's to reach A145382. Read the binary digits from right to left. a(n) is the decimal equivalent of the result.
All entries are even, i.e., members of A005843.
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LINKS
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FORMULA
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EXAMPLE
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37->100101->change digits 011010->read from right to left 010110->22 281->100011001->change digits 011100110->read from right to left 011001110->206
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MAPLE
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P:=proc(i) local a, b, j, k, n; for n from 1 by 1 to i do a:=convert(ithprime(n), binary); j:=length(a); b:=convert(a, string); k:=""; while j>0 do if substring(b, j)="1" then k:=cat(k, "0"); else k:=cat(k, "1"); fi; j:=j-1; od; a:=convert(k, decimal, binary); print(a); od; end: P(100);
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MATHEMATICA
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FromDigits[Reverse@ BitNot@ IntegerDigits[#, 2] + 2, 2] & /@ Prime@ Range@ 71 (* Michael De Vlieger, Apr 22 2015 *)
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PROG
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(Python)
from sympy import prime
def A159006(n): return -int((s:=bin(prime(n))[-1:1:-1]), 2)-1+2**len(s) # Chai Wah Wu, Feb 04 2022
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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