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A352751 Modified Sisyphus function of order 4: a(n) is the concatenation of (number of digits of n)(number digits of n congruent to 0 modulo 4)(number of digits of n congruent to 1 modulo 4)(number of digits of n congruent to 2 modulo 4)(number of digits of n congruent to 3 modulo 4). 0
11000, 10100, 10010, 10001, 11000, 10100, 10010, 10001, 11000, 10100, 21100, 20200, 20110, 20101, 21100, 20200, 20110, 20101, 21100, 20200, 21010, 20110, 20020, 20011, 21010, 20110, 20020, 20011, 21010, 20110, 21001, 20101, 20011, 20002, 21001, 20101, 20011, 20002, 21001, 20101, 22000, 21100, 21010 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If we start with n and repeatedly apply the map i -> a(i), we eventually get one of three cycles:  {51220}, {50410, 52111, 53200}, or {51301}

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..42.

EXAMPLE

11 has two digits, both congruent to 1 modulo 4, so a(11) = 20200.

a(20) = 21010.

a(30) = 21001.

a(1111123567) = 100622.

PROG

(Python)

def a(n, order=4):

    d, m = list(map(int, str(n))), [0]*order

    for di in d: m[di%order] += 1

    return int(str(len(d)) + "".join(map(str, m)))

print([a(n) for n in range(37)]) # Michael S. Branicky, Apr 01 2022

CROSSREFS

Cf. A073053 (Sisyphus), A171797, A171798, A171813, A055642, A196563, A196564, A308002, A350709.

Sequence in context: A104323 A252039 A252033 * A266983 A227865 A267777

Adjacent sequences:  A352748 A352749 A352750 * A352752 A352753 A352754

KEYWORD

nonn,base,easy

AUTHOR

Matthew E. Coppenbarger, Apr 01 2022

STATUS

approved

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Last modified August 10 00:32 EDT 2022. Contains 356026 sequences. (Running on oeis4.)