A095258 -id:A095258 - cp's OEIS frontend

A253425 Lengths of runs of identical terms in A253415.

1, 1, 6, 11, 18, 12, 5, 22, 91, 143, 1, 93, 370, 182, 20, 20, 315, 332, 973, 157, 1223, 1807, 325, 4044, 7412, 11211, 4600, 2176, 14848, 4659, 3123, 10852, 1678, 20862, 3348

Offset: 1

Reinhard Zumkeller, Dec 31 2014

Cf. A253415, A095258.

import Data.List (group)
a253425 n = a253425_list !! (n-1)
a253425_list = map length $ group a253415_list

c[] = 0; c[1] = j = 1; u = 2; s = 3; Most@ Tally[#][[All, -1]] &@ Reap[Do[d = Divisors[s]; k = 1; While[c[d[[k]]] > 0, k++]; Set[k, d[[k]]]; Set[c[k], i]; If[k == u, While[c[u] > 0, u++]]; Sow[u]; j = k; s += k, {i, 2, 2^12}]][[-1, -1]] (* _Michael De Vlieger, Jan 23 2022 *)

from itertools import islice
from sympy import divisors
def A253425_gen(): # generator of terms
    bset, l, m, s = {1}, 0, 2, 3
    while True:
        for d in divisors(s):
            if d not in bset:
                bset.add(d)
                if m in bset:
                    yield l
                    l = 1
                    while m in bset:
                        m += 1
                else:
                    l += 1
                s += d
                break
A253425_list = list(islice(A253425_gen(),20)) # Chai Wah Wu, Jan 25 2022

a(14)-a(35) from Michael De Vlieger, Jan 23 2022

A308746 a(1) = 1, and for n > 1, a(n) is the greatest k > 0 such that (a(1), ..., a(n-1)) can be split into k chunks of contiguous terms and those chunks have the same sum.

Original entry on oeis.org

1, 1, 2, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 4, 2, 5, 1, 6, 7, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 5, 1, 1, 1, 2, 2, 2, 2, 2, 6, 2, 2, 2, 4, 2, 7, 1, 2, 2, 2, 2, 1, 1, 8, 2, 2, 3, 3, 9, 3, 3, 3, 10, 2, 2, 2

Offset: 1

Rémy Sigrist, Jun 21 2019

nonn

For any n > 0, a(n) divides Sum_{k = 1..n-1} a(k).

Is this sequence unbounded?

			The first terms, alongside the corresponding chunks, are:
  n   a(n)  Chunks (separated by pipes)
  --  ----  -------------------------------------
   1     1
   2     1  1
   3     2  1|1
   4     2  1 1|2
   5     3  1 1|2|2
   6     1  1 1 2 2 3
   7     1  1 1 2 2 3 1
   8     1  1 1 2 2 3 1 1
   9     2  1 1 2 2|3 1 1 1
  10     1  1 1 2 2 3 1 1 1 2
  11     1  1 1 2 2 3 1 1 1 2 1
  12     1  1 1 2 2 3 1 1 1 2 1 1
  13     1  1 1 2 2 3 1 1 1 2 1 1 1
  14     3  1 1 2 2|3 1 1 1|2 1 1 1 1
  15     1  1 1 2 2 3 1 1 1 2 1 1 1 1 3
  16     2  1 1 2 2 3 1 1|1 2 1 1 1 1 3 1
  17     4  1 1 2 2|3 1 1 1|2 1 1 1 1|3 1 2
  18     2  1 1 2 2 3 1 1 1 2|1 1 1 1 3 1 2 4
  19     5  1 1 2 2|3 1 1 1|2 1 1 1 1|3 1 2|4 2
  20     1  1 1 2 2 3 1 1 1 2 1 1 1 1 3 1 2 4 2 5

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Colored scatterplot of the first 1000000 terms (where the color is function of Sum_{k = 1..n-1} a(k) / a(n))
Rémy Sigrist, PARI program for A308746

Cf. A095258.

PARI
```
See Links section.
```

cp's OEIS Frontend

A253425 Lengths of runs of identical terms in A253415.

Views

Author

Keywords

Crossrefs

Programs

Haskell

Mathematica

Python

Extensions

A308746 a(1) = 1, and for n > 1, a(n) is the greatest k > 0 such that (a(1), ..., a(n-1)) can be split into k chunks of contiguous terms and those chunks have the same sum.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI