A344856 Bitwise XOR of prime(n) and n^2.
3, 7, 12, 23, 18, 41, 32, 83, 70, 121, 102, 181, 128, 239, 206, 309, 282, 377, 298, 471, 496, 427, 578, 537, 528, 705, 702, 891, 804, 1013, 958, 1155, 1224, 1039, 1116, 1415, 1476, 1287, 1366, 1773, 1570, 1617, 1926, 1873, 1836, 2179, 2162, 2527, 2434, 2337
Offset: 1
Examples
For n=3, a(3) is prime(3) XOR 3^2 = 5 XOR 9 or b(0101) XOR b(1001) = (b)1100, which in base 10 is 12.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
- Chris von Csefalvay, Bitwise prime-square sequences ("Jellyfish Hearts").
- Wikipedia, Bitwise operation
Programs
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Maple
a:= n-> Bits[Xor](n^2, ithprime(n)): seq(a(n), n=1..50); # Alois P. Heinz, May 30 2021
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Mathematica
a[n_] := BitXor[n^2, Prime[n]]; Array[a, 50] (* Amiram Eldar, Jun 05 2021 *)
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PARI
A344856(n) = bitxor(prime(n),n*n); \\ Antti Karttunen, Jun 05 2021
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Python
from sympy import primerange, prime import numpy def a_vector(n): primes = list(primerange(0, prime(n))) squares = [x ** 2 for x in range(1, n)] return numpy.bitwise_xor(primes, squares) -
Python
from sympy import prime def A344856(n): return prime(n) ^ n**2 # Chai Wah Wu, Jun 12 2021
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