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

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

Author

Christoph Schreier, Apr 15 2020

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Cf. A000040, A112591, A145382, A175330.

Programs

Maple

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

Mathematica

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

PARI

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

Python

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)

Formula

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