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

1,2

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.

Links

Table of n, a(n) for n=1..37.

Example

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

Prog

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

Crossrefs

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

Sequence in context: A310128 A310129 A310130 * A196068 A242239 A123089

Adjacent sequences: A298815 A298816 A298817 * A298819 A298820 A298821

Keyword

nonn,base

Author

Alex Ratushnyak, Jan 26 2018

Status

approved