A169810 -id:A169810 - cp's OEIS frontend

A283750 a(n) = n^2 XOR (n + 1)^2.

1, 5, 13, 25, 9, 61, 21, 113, 17, 53, 29, 233, 57, 109, 37, 481, 33, 101, 45, 249, 41, 93, 1013, 81, 49, 213, 125, 457, 89, 205, 69, 1985, 65, 197, 77, 473, 73, 253, 85, 945, 209, 117, 477, 169, 121, 4013, 229, 417, 97, 165, 1005, 185, 105, 413, 181, 1937, 241, 405, 189, 905, 153, 397, 133, 8065, 129, 389, 141, 921

Offset: 0

Ilya Gutkovskiy, Mar 15 2017

nonn

XOR the binary representations of n^2 and (n + 1)^2.

Antti Karttunen, Table of n, a(n) for n = 0..20000
Ilya Gutkovskiy, Extended graphical example
Eric Weisstein's World of Mathematics, XOR
Index entries for sequences related to binary expansion of n

Cf. A000290, A003987, A016813 (records), A038712, A112591, A169810.

Cf. also A379007.

Table[BitXor[n^2, (n + 1)^2], {n, 0, 67}]

A283750(n) = bitxor(n^2, (n+1)^2); \\ Indranil Ghosh, Mar 15 2017, Antti Karttunen, Dec 16 2024

def A283750(n): return (n**2)^(n + 1)**2 # Indranil Ghosh, Mar 15 2017

a(n) = A000290(n) XOR A000290(n+1).

A280211 a(n) = n*(2^(n^2)).

Original entry on oeis.org

0, 2, 32, 1536, 262144, 167772160, 412316860416, 3940649673949184, 147573952589676412928, 21760664753063325144711168, 12676506002282294014967032053760, 29243015907268149203883755326167580672, 267608942382367477698428619271780338071764992, 9727754898074489823563726246559579778829887006048256

Offset: 0

Indranil Ghosh, Jan 06 2017

a(n) =  n with the bits shifted to the left by n^2 places (new bits on the right hand side are zeros) i.e, a(n) = n<<(n**2).
a(n) is always even.
a(n) mod 32 = 0 for n>=2.

Indranil Ghosh, Table of n, a(n) for n = 0..50
MSDN, Bitwise Left Shift Operator
Stack Overflow Use of Bit Shifting Operators

Cf. A002416, A213541, A007745, A169810.

Table[n*2^n^2,{n,0,20}] (* Harvey P. Dale, Jan 01 2021 *)

Python
```
a=lambda n: n<<(n**2)
```

a(n) = n*(2^(n^2)).

a(n) = n*A002416(n). - Omar E. Pol, Jan 06 2017

A344856 Bitwise XOR of prime(n) and n^2.

Original entry on oeis.org

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

Chris von Csefalvay, May 30 2021

This is effectively the bitwise XOR of A000040 and A000290.

			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.

Chai Wah Wu, Table of n, a(n) for n = 1..10000
Chris von Csefalvay, Bitwise prime-square sequences ("Jellyfish Hearts").
Wikipedia, Bitwise operation

Cf. A000040, A000290, A003987, A070883, A169810.

a:= n-> Bits[Xor](n^2, ithprime(n)):
seq(a(n), n=1..50);  # Alois P. Heinz, May 30 2021

a[n_] := BitXor[n^2, Prime[n]]; Array[a, 50] (* Amiram Eldar, Jun 05 2021 *)

A344856(n) = bitxor(prime(n),n*n); \\ Antti Karttunen, Jun 05 2021

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)

from sympy import prime
def A344856(n): return prime(n) ^ n**2 # Chai Wah Wu, Jun 12 2021

a(n) = prime(n) XOR n^2.

a(n) = A003987(A000040(n), A000290(n)).

cp's OEIS Frontend

A283750 a(n) = n^2 XOR (n + 1)^2.

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A280211 a(n) = n*(2^(n^2)).

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A344856 Bitwise XOR of prime(n) and n^2.

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