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A159006 Transformation of prime(n): flip digits in the binary representation, revert the sequence of digits, and convert back to decimal. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
LINKS
FORMULA
a(n) = A036044(prime(n)). - Michel Marcus, Apr 22 2015
EXAMPLE
37->100101->change digits 011010->read from right to left 010110->22 281->100011001->change digits 011100110->read from right to left 011001110->206
MAPLE
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);
MATHEMATICA
FromDigits[Reverse@ BitNot@ IntegerDigits[#, 2] + 2, 2] & /@ Prime@ Range@ 71 (* Michael De Vlieger, Apr 22 2015 *)
PROG
(PARI) a(n)=fromdigits(Vecrev(apply(n->1-n, binary(prime(n)))), 2) \\ Charles R Greathouse IV, Apr 22 2015
(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
CROSSREFS
Sequence in context: A292129 A291970 A281981 * A291968 A226171 A284280
KEYWORD
easy,nonn,base
AUTHOR
EXTENSIONS
Edited by R. J. Mathar, Apr 06 2009
STATUS
approved

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Last modified July 14 02:38 EDT 2024. Contains 374291 sequences. (Running on oeis4.)