A071770 Tersum n + [n/3] (answer recorded in base 10).

0, 1, 2, 4, 5, 3, 8, 6, 7, 12, 13, 14, 16, 17, 15, 11, 9, 10, 24, 25, 26, 19, 20, 18, 23, 21, 22, 36, 37, 38, 40, 41, 39, 44, 42, 43, 48, 49, 50, 52, 53, 51, 47, 45, 46, 33, 34, 35, 28, 29, 27, 32, 30, 31, 72, 73, 74, 76, 77, 75, 80, 78, 79, 57, 58, 59, 61, 62, 60, 56, 54, 55, 69, 70

Offset: 0

Author

Paul D. Hanna, Jun 04 2002

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..19682
• P. Mathonet, M. Rigo, M. Stipulanti and N. Zénaïdi, On digital sequences associated with Pascal's triangle, arXiv:2201.06636 [math.NT], 2022.
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A004482.

Inverse permutation to A370932.

Programs

Maple

a:= n-> (l-> add(irem(l[i]+l[i-1], 3)*3^(i-2),
         i=2..nops(l)))([convert(n, base, 3)[], 0]):
seq(a(n), n=0..73);  # Alois P. Heinz, Aug 07 2024

PARI

a(n)={if(n==0, 0, fromdigits((digits(n,3) + concat([0],digits(n\3,3)))%3,3))} \\ Andrew Howroyd, Aug 06 2024

Python

from sympy.ntheory import digits
def a(n):
    d = digits(n, 3)[1:]
    return int(str(d[0]) + "".join(str((d[i]+d[i-1])%3) for i in range(1, len(d))), 3)
print([a(n) for n in range(75)]) # Michael S. Branicky, Aug 07 2024

Formula

Tersum m + n: write m and n in base 3 and add mod 3 with no carries, e.g. 5 + 8 = "21" + "22" = "10" = 1. See A004482 for references.

Extensions

a(27) corrected by Sean A. Irvine, Aug 06 2024