A298818 a(n) is the binary XOR of all n-bit triangular numbers.

1, 3, 6, 5, 9, 62, 70, 204, 348, 586, 1770, 3582, 6974, 9046, 22486, 12225, 54977, 97140, 201076, 34728, 347048, 1031920, 2250480, 10857648, 24157360, 40826080, 112612576, 21772545, 130349313, 1060428174, 1126848910, 1106260993, 2017932289, 3773334644, 13412500596, 6378289192, 37614057512

Offset: 1

Author

Alex Ratushnyak, Jan 26 2018

Keywords

• nonn
• base

Comments

XOR is the binary exclusive-or operator.

Note { a(20), a(21) } = { 34728, 347048 }. First 3 and last digits are the same.

Also { a(27), a(31) } = { 112612576, 1126848910 }. First 4 decimal digits are the same.

Examples

			There are two 4-bit triangular numbers, namely 10 and 15; a(4) = (10 XOR 15) = 5.
		

Crossrefs

Cf. A000217, A007088, A070939, A298816, A298817.

Programs

PARI

a(n) = {my(x = 0); for (k=2^(n-1), 2^n-1, if (ispolygonal(k, 3), x = bitxor(x, k)); ); x; } \\ Michel Marcus, Feb 13 2018

Python

i = n = x = L = 1
while L < 47:
    i+=1
    nextn = i*(i+1)//2
    if (nextn ^ n) > n:
        print(x, end=', ')
        x = 0
        prevL = L
        L = len(bin(nextn))-2
        for j in range(prevL, L-1):  print(0, end=', ')
    n = nextn
    x ^= n