A145382 -id:A145382 - cp's OEIS frontend

A171008 Write the n-th prime in binary and change all 0's to 1's and all 1's to 0's.

1, 0, 10, 0, 100, 10, 1110, 1100, 1000, 10, 0, 11010, 10110, 10100, 10000, 1010, 100, 10, 111100, 111000, 110110, 110000, 101100, 100110, 11110, 11010, 11000, 10100, 10010, 1110, 0, 1111100, 1110110, 1110100, 1101010, 1101000, 1100010, 1011100

Offset: 1

N. J. A. Sloane, Sep 03 2010

See A145382 for the decimal equivalents.

A171008 := proc(n) local p2 ; p2 := convert(ithprime(n),base,2) ; add( (1-op(i,p2)) *10^(i-1),i=1..nops(p2)) ; end proc: seq(A171008(n),n=1..80) ; # R. J. Mathar, Sep 04 2010

FromDigits/@(IntegerDigits[#,2]&/@Prime[Range[40]]/.{0->1,1->0}) (* Harvey P. Dale, Aug 19 2017 *)

a(n)=my(v=binary(prime(n)),k=1/10);sum(i=0,#v-1,k*=10;(1-v[ #v-i])*k) \\ Charles R Greathouse IV, Sep 08 2010

More terms from Charles R Greathouse IV and R. J. Mathar, Sep 04 2010

A334143 a(n) = bitwise NOR of prime(n) and prime(n+1).

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 12, 8, 0, 0, 0, 18, 20, 16, 0, 0, 0, 0, 56, 48, 48, 32, 36, 6, 26, 24, 16, 16, 2, 0, 0, 116, 116, 96, 104, 96, 64, 88, 80, 64, 72, 64, 0, 58, 56, 40, 32, 0, 24, 18, 16, 0, 4, 4, 248, 240, 240, 224, 226, 228, 192, 200, 200, 192, 194, 128, 164

Offset: 1

Christoph Schreier, Apr 15 2020

			a(6) = prime(6) NOR prime(7) = 13 NOR 17 = 2.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Wikipedia, Bitwise operation

Cf. A000040, A112591, A145382, A175330.

a:= n-> Bits[Nor](ithprime(n), ithprime(n+1)):
seq(a(n), n=1..70);  # Alois P. Heinz, Apr 15 2020

A334143[n_]:=With[{b=BitOr[Prime[n],Prime[n+1]]},2^BitLength[b]-b-1];Array[A334143,100] (* Paolo Xausa, Oct 13 2023 *)

a(n) = my(x=bitor(prime(n), prime(n+1))); bitneg(x, #binary(x)); \\ Michel Marcus, Apr 16 2020

def NORprime(n):
    s = str(bin(primes[n]))[2:]
    t = str(bin(primes[n-1]))[2:]
    k = (len(s) -  len(t))
    t = k*'0' + t
    r = ''
    for i in range(len(s)):
        if s[i] == t[i] and s[i] == '0':
            r += '1'
        else:
            r += '0'
    return int(r,2)

a(n) = A035327(A175329(n)).

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

Original entry on oeis.org

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

Paolo P. Lava & Giorgio Balzarotti, Apr 02 2009

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.

			37->100101->change digits 011010->read from right to left 010110->22 281->100011001->change digits 011100110->read from right to left 011001110->206

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

Cf. A036044, A098957, A145382.

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);

FromDigits[Reverse@ BitNot@ IntegerDigits[#, 2] + 2, 2] & /@ Prime@ Range@ 71 (* Michael De Vlieger, Apr 22 2015 *)

a(n)=fromdigits(Vecrev(apply(n->1-n,binary(prime(n)))),2) \\ Charles R Greathouse IV, Apr 22 2015

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

a(n) = A036044(prime(n)). - Michel Marcus, Apr 22 2015

Edited by R. J. Mathar, Apr 06 2009

cp's OEIS Frontend

A171008 Write the n-th prime in binary and change all 0's to 1's and all 1's to 0's.

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A334143 a(n) = bitwise NOR of prime(n) and prime(n+1).

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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.

Views

Author

Keywords

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Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula

Extensions