A322845 Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has distinct digits in factorial base.

1, 3, 2, 8, 5, 9, 4, 6, 7, 12, 10, 13, 33, 34, 43, 24, 22, 45, 23, 44, 38, 29, 17, 50, 18, 28, 39, 46, 21, 25, 42, 26, 20, 47, 30, 16, 51, 31, 15, 52, 49, 19, 27, 40, 37, 48, 53, 14, 32, 35, 11, 56, 54, 55, 60, 41, 36, 65, 173, 182, 174, 64, 291, 170, 68, 287

Offset

1,2

Comments

In other words, for any n > 0, a(n) + a(n+1) belongs to A321682.

Apparently, all the positive integers appear in the sequence.

This sequence has interesting graphical features (see scatterplots in Links section).

This sequence is to A321682 what A228730 is to A002113.

Links

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

Rémy Sigrist, Scatterplot of the first 181425 terms

Rémy Sigrist, Scatterplot of the first 19958408 terms

Rémy Sigrist, C program for A322845

Index entries for sequences related to factorial base representation

Example

The first terms, alongside the factorial representation of a(n)+a(n+1), are:
  n   a(n)  fact(a(n)+a(n+1))
  --  ----  -----------------
   1     1              (2,0)
   2     3              (2,1)
   3     2            (1,2,0)
   4     8            (2,0,1)
   5     5            (2,1,0)
   6     9            (2,0,1)
   7     4            (1,2,0)
   8     6            (2,0,1)
   9     7            (3,0,1)
  10    12            (3,2,0)
  11    10            (3,2,1)
  12    13          (1,3,2,0)

Prog

(C) See Links section.

Crossrefs

Cf. A002113, A228730, A321682.

Sequence in context: A125980 A126320 A336478 * A307705 A240447 A135992

Adjacent sequences: A322842 A322843 A322844 * A322846 A322847 A322848

Keyword

nonn,base,look

Author

Rémy Sigrist, Dec 29 2018

Status

approved