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

Author

Rémy Sigrist, Dec 29 2018

Keywords

• nonn
• base
• look

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.

Examples

			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)
		

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

Crossrefs

Cf. A002113, A228730, A321682.

Programs

C

// See Links section.