A350709 Modified Sisyphus function of order 3: a(n) is the concatenation of (number of digits of n)(number digits of n congruent to 0 modulo 3)(number of digits of n congruent to 1 modulo 3)(number of digits of n congruent to 2 modulo 3).

1100, 1010, 1001, 1100, 1010, 1001, 1100, 1010, 1001, 1100, 2110, 2020, 2011, 2110, 2020, 2011, 2110, 2020, 2011, 2110, 2101, 2011, 2002, 2101, 2011, 2002, 2101, 2011, 2002, 2101, 2200, 2110, 2101, 2200, 2110, 2101, 2200

Offset

0,1

Comments

If we start with n and repeatedly apply the map i -> a(i), we eventually get the cycle {4031, 4112, 4220}

References

M. E. Coppenbarger, Iterations of a modified Sisyphus function, Fib. Q., 56 (No. 2, 2018), 130-141.

Links

Table of n, a(n) for n=0..36.

Example

11 has two digits, both congruent to 1 modulo 3, so a(11) = 2020.
a(20) = 2101.
a(30) = 2200.
a(1111123567) = 10262.

Prog

(Python)
def a(n):
    d, m = list(map(int, str(n))), [0, 0, 0]
    for di in d: m[di%3] += 1
    return int(str(len(d)) + "".join(map(str, m)))
print([a(n) for n in range(37)]) # Michael S. Branicky, Mar 28 2022

Crossrefs

Cf. A073053 (Sisyphus), A171797, A171798, A171813, A055642, A196563, A196564, A308002.

Sequence in context: A280612 A281039 A078199 * A271472 A147816 A050926

Adjacent sequences: A350706 A350707 A350708 * A350710 A350711 A350712

Keyword

nonn,base,easy

Author

Matthew E. Coppenbarger, Mar 28 2022

Status

approved