A159006 Transformation of prime(n): flip digits in the binary representation, revert the sequence of digits, and convert back to decimal.

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

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

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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

Cf. A036044, A098957, A145382.

Sequence in context: A292129 A291970 A281981 * A291968 A226171 A284280

Adjacent sequences: A159003 A159004 A159005 * A159007 A159008 A159009

Keyword

easy,nonn,base

Author

Paolo P. Lava & Giorgio Balzarotti, Apr 02 2009

Extensions

Edited by R. J. Mathar, Apr 06 2009

Status

approved