A309063 -id:A309063 - cp's OEIS frontend

A309072 a(n) is the concatenation of the initial digit of A247476(k) for k = A309063(n)..A309063(n+1)-1.

12132453674859161724822942, 121121, 121121, 2342536434553643455364345536436553789651617788966917178682392737988131273298, 78912142738493, 912112112192, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121

Offset: 1

Rémy Sigrist, Jul 10 2019

For any n > 0:
- a(n) has an even number of digits,
- for any digit d appearing in a(n):
    - d appears an even number of times,
    - each pair of digits d is separated by d other digits,
- a(n) cannot be split into two parts with these properties.
The distribution of the first million values is as follows:
  Freq.   Length   Value
  ------  -------  --------------------------------------------------------------
  932062        6                                                          121121
   44451       38                          78912142778498923727318198971711218297
   19557       12                                                    891211211819
    3915       12                                                    912112112192
       3       14                                                  78912142738493
       1       26                                      12132453674859161724822942
       1       76  234253643455364345536434553643..966917178682392737988131273298
       1      280  789121427784989237213188991211..392931211212392931211212392131
       1      712  121322432234223322432234223322..819191717881219277988131273298
       1     2200  789121427784989237213188991211..392931211212392931211212392131
       1     6438  121322432234223322432234223322..798916167718196687792562387539
       1    64958  121322432234223322432234223322..819191717881219277988131273298
       1   112810  678912162768798916167718196687..687989161677181968971711218297
       1   563478  121322432234223322432234223322..177669883476364987896612172869
       1   744654  678912162768798916167718196687..819191717881219277988131273298
       1  2095732  789121427784989237273181989712..392931211212392931211212392131
       1  5830936  234253243252332243223422332243..177669883476364987896612172869

			For n = 2:
- A309063(2) = 27 and A309063(3)-1 = 32,
- A000030(A247476(27)) = A000030(13) = 1,
- A000030(A247476(28)) = A000030(25) = 2,
- A000030(A247476(29)) = A000030(14) = 1,
- A000030(A247476(30)) = A000030(15) = 1,
- A000030(A247476(31)) = A000030(26) = 2,
- A000030(A247476(32)) = A000030(16) = 1,
- hence a(2) = 121121.

Rémy Sigrist, C program for A309072

Cf. A000030, A247476, A309063.

C
```
See Links section.
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A309073 Split the sequence A247476 into nonempty chunks of minimal length such that for d = 1..9, the number of terms with leading digit d is even; a(n) is the length of the n-th chunk.

Original entry on oeis.org

26, 6, 6, 76, 14, 12, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 712, 38, 280, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 1

Rémy Sigrist, Jul 10 2019

This sequence corresponds to the first difference of A309063.

			See illustration of first terms in Links section.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Illustration of first terms

Cf. A247476, A309063, A309072.

a(n) = A309063(n+1) - A309063(n).

a(n) = A055642(A309072(n)).

cp's OEIS Frontend

A309072 a(n) is the concatenation of the initial digit of A247476(k) for k = A309063(n)..A309063(n+1)-1.

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