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.

User: Peter Stikker

Peter Stikker's wiki page.

Peter Stikker has authored 2 sequences.

A309180 Unsuspected numbers to check in the Collatz conjecture.

Original entry on oeis.org

61, 91, 205, 253, 325, 415, 433, 577, 637, 739, 901, 919, 991, 1063, 1171, 1225, 1333, 1387, 1549, 1663, 1711, 1837, 1873, 1891, 2035, 2125, 2197, 2287, 2359, 2449, 2521, 2683, 2791, 2845, 3007, 3169, 3187, 3277, 3331, 3349, 3439, 3493
Offset: 1

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Author

Peter Stikker, Jul 15 2019

Keywords

Comments

The sequence is constructed using the following steps:
Start at 1, and color it blue. Go through the Collatz algorithm, highlight each number that is not in 'blue' in 'red' until you reach an already 'red' number or lower number that is 'blue'. Color the next uncolored number 'blue' and repeat.
So starting at 1, 1 becomes blue, then 4 becomes red, 2 becomes red and move to next number. Next uncolored number is 3, so 3 becomes blue. Then 10 becomes red, 5 becomes red, 16 red, 8 red, and 4 is already red so done. Next uncolored number is 6, so 6 becomes blue, etc.
For any number k the expected colors are:
red if k (mod 18) is equal to 2, 4, 5, 8, 10, 11, 13, 14, 16, or 17.
blue if k (mod 18) is equal to 0, 1, 3, 6, 7, 9, 12, or 15
The list here are the numbers that do not fit this pattern.
Observation:
For up to at least 180000 only numbers of the format k (mod 18) = 1 and k (mod 18) = 7 were not fitting the pattern, they were all red instead of blue.

Links

Crossrefs

Cf. A014682 (the Collatz function). So far the numbers are all of the form 6n + 1, so this would be a subset of A016921.

Programs

  • PARI
    isokb(k) = (k==0) || (k==1) || (k==3) || (k==6) || (k==7) || (k==9) || (k==12) || (k==15);
isokr(k) = (k==2) || (k==4) || (k==5) || (k==8) || (k==10) || (k==11) || (k==13) || (k==14) || (k==16) || (k==17);
f(n) = if(n%2, 3*n+1, n/2);
nocolor(n, vred, vblue) = !vecsearch(vred, n) && !vecsearch(vblue, n);
chk(nn) = {vblue = []; vred = []; for (n=1, nn, if (nocolor(n, vred, vblue), ok = 1; vblue = vecsort(concat(vblue, n),,8); ntodo = n; while (1, m = f(ntodo); if (vecsearch(vred, m), break); if ((m(!isokb(x%18)), vblue); vr = select(x->(!isokr(x%18)), vred); select(x->x<=nn, vecsort(concat(vr, vb)));} \\ Michel Marcus, Jul 17 2019

A318613 Length of iterations of positive integers which do not appear in a Collatz sequence starting from a smaller positive integer.

Original entry on oeis.org

0, 1, 7, 8, 16, 19, 9, 17, 20, 20, 7, 10, 23, 111, 18, 26, 21, 21, 34, 8, 29, 16, 11, 24, 112, 112, 32, 19, 107, 27, 14, 22, 115, 14, 35, 35, 22, 9, 30, 17, 17, 12, 118, 25, 25, 38, 113, 113, 69, 33, 33, 20, 20, 46, 108, 46, 121, 28, 28, 41, 15, 15
Offset: 1

Views

Author

Peter Stikker, Aug 30 2018

Keywords

Comments

The sequence of the length of the iteration in the Collatz sequence is known as A006577, and the sequence of positive integers which do not appear in a Collatz sequence starting from a smaller positive integer is listed as A177729. This sequence is basically the combination of the two. Taking the sequence A177729 as input and then listing the length of the iteration for those (from A006577).

Crossrefs

Cf. A177729, A006577.
Almost the same as A127933.

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