A335497 a(1) = 1, and for any n > 0, a(n+1) is the number of times the decimal representation of a(n) appears in the concatenation of the first n terms, possibly with overlap.

1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 12, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 10, 2, 11, 4, 3, 3, 4, 4, 5, 3, 5, 4, 6, 3, 6, 4, 7, 3, 7, 4, 8, 3, 8, 4, 9, 3, 9, 4, 10, 3, 10, 4, 11, 5, 5, 6, 5, 7, 5, 8, 5, 9, 5, 10, 5, 11, 6, 6

Offset

1,3

Comments

This sequence is a variant of A276457.

This sequence is unbounded.

It seems that lim sup a(n)/(n*log(n)) = 0.03 approximately. - Ya-Ping Lu, Dec 16 2021

Links

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

Rémy Sigrist, Logarithmic scatterplot of the first 1000000 terms

Rémy Sigrist, Perl program for A335497

Example

The first terms, alongside their concatenations with a star in front of each occurrence of a(n), are:
  n   a(n)  cat(a(1)...a(n))
  --  ----  ---------------------------------
   1     1  *1
   2     1  *1*1
   3     2  11*2
   4     1  *1*12*1
   5     3  1121*3
   6     1  *1*12*13*1
   7     4  112131*4
   8     1  *1*12*13*14*1
   9     5  11213141*5
  ...
  17     9  1121314151617181*9
  18     1  *1*12*13*14*15*16*17*18*19*1
  19    10  112131415161718191*10
  20     1  *1*12*13*14*15*16*17*18*19*1*10*1
  21    12  1*12131415161718191101*12
  22     2  11*21314151617181911011*2*2

Prog

(Perl) See Links section.
(Python)
a1 = 1; print(a1, end =', '); S = str(a1)
for n in range(2, 100): ct = S.count(str(a1)); S += str(ct); print(ct, end = ', '); a1 = ct # Ya-Ping Lu, Dec 16 2021

Crossrefs

Cf. A179801, A276457.

Sequence in context: A158416 A318225 A360257 * A309872 A359031 A248034

Adjacent sequences: A335494 A335495 A335496 * A335498 A335499 A335500

Keyword

nonn,base

Author

Rémy Sigrist, Jun 14 2020

Status

approved