cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A352752 a(n) is the smallest nonnegative number that requires n applications of the modified Sisyphus function of order 3, x -> A350709(x) to reach any number in the cycle {4031, 4112, 4220}.

Original entry on oeis.org

4031, 1001, 0, 10, 1000000000
Offset: 0

Views

Author

Matthew E. Coppenbarger, Apr 01 2022

Keywords

Comments

The next term, a(5), is 1 0^100 1^9 2^10, a number with 120 digits, is too large to display.

Examples

			0 -> 1100 -> 4220 reaches an element of the cycle {4031, 4112, 4220} in two iterates and must be the smallest, so a(2) = 0

References

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

Crossrefs

Cf. A350709.

A375208 Modified Sisyphus function of order 5.

Original entry on oeis.org

110000, 101000, 100100, 100010, 100001, 110000, 101000, 100100, 100010, 100001, 211000, 202000, 201100, 201010, 201001, 211000, 202000, 201100, 201010, 201001, 210100, 201100, 200200, 200110, 200101, 210100, 201100, 200200, 200110, 200101, 210010, 201010, 200110, 200020, 200011, 210010, 201010, 200110, 200020, 200011, 210001, 201001, 200101, 200011, 200002
Offset: 0

Views

Author

Matt Coppenbarger, Oct 16 2024

Keywords

Comments

a(n) is the concatenation of the number of digits in n with number of digits of n congruent to k modulo 5 for each k from 0 to 4 in turn. See Example.
If we start with n and repeatedly apply the map i -> a(i), we eventually get the cycle {613200, 622110}.

Examples

			11 has two digits, both congruent to 1 modulo 5, so a(11) = 202000.
a(20) = 210100.
a(30) = 210010.
a(2527200000) = 1060400.

Links

Crossrefs

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

Programs

  • Maple
    a:= n-> (l-> parse(cat(nops(l), seq(add(`if`(irem(i, 5)=k
          , 1, 0), i=l), k=0..4))))(convert(n, base, 10)):
seq(a(n), n=0..44);  # Alois P. Heinz, Oct 23 2024
  • Python
    # based on Michael S. Branicky in A350709
def a(n, order=5):
    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)])
  • Python
    from collections import Counter
def A375208(n):
    s = str(n)
    c = Counter(int(d)%5 for d in s)
    return int(str(len(s))+''.join(str(c[i]) for i in range(5))) # Chai Wah Wu, Nov 26 2024

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).

Original entry on oeis.org

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
Offset: 0

Views

Author

Matthew E. Coppenbarger, Apr 01 2022

Keywords

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}

Examples

			11 has two digits, both congruent to 1 modulo 4, so a(11) = 20200.
a(20) = 21010.
a(30) = 21001.
a(1111123567) = 100622.

References

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

Crossrefs

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

Programs

  • 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
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.