%I #23 Feb 05 2022 02:15:09
%S 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,
%T 20,36,56,0,62,110,46,86,22,70,58,26,74,50,82,2,124,92,28,52,4,56,88,
%U 104,8,112,32,254,62,158,30,174,206,78,182,102,38,198,134,90,234,74,138,242
%N Transformation of prime(n): flip digits in the binary representation, revert the sequence of digits, and convert back to decimal.
%C 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.
%C All entries are even, i.e., members of A005843.
%H Michael De Vlieger, <a href="/A159006/b159006.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A036044(prime(n)). - _Michel Marcus_, Apr 22 2015
%e 37->100101->change digits 011010->read from right to left 010110->22 281->100011001->change digits 011100110->read from right to left 011001110->206
%p 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);
%t FromDigits[Reverse@ BitNot@ IntegerDigits[#, 2] + 2, 2] & /@ Prime@ Range@ 71 (* _Michael De Vlieger_, Apr 22 2015 *)
%o (PARI) a(n)=fromdigits(Vecrev(apply(n->1-n,binary(prime(n)))),2) \\ _Charles R Greathouse IV_, Apr 22 2015
%o (Python)
%o from sympy import prime
%o def A159006(n): return -int((s:=bin(prime(n))[-1:1:-1]),2)-1+2**len(s) # _Chai Wah Wu_, Feb 04 2022
%Y Cf. A036044, A098957, A145382.
%K easy,nonn,base
%O 1,1
%A _Paolo P. Lava_ & _Giorgio Balzarotti_, Apr 02 2009
%E Edited by _R. J. Mathar_, Apr 06 2009