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

Author

Rémy Sigrist, Jul 10 2019

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

• Rémy Sigrist, C program for A309072

Crossrefs

Cf. A000030, A247476, A309063.

Programs

C

See Links section.