A332843 Lexicographically earliest sequence of positive terms such that a(4n+1) is the sum of the next three terms, those three terms having the property that each of them is a substring of a(4n+1).

15, 5, 5, 5, 19, 1, 9, 9, 150, 50, 50, 50, 182, 18, 82, 82, 191, 9, 91, 91, 195, 5, 95, 95, 199, 1, 99, 99, 1500, 500, 500, 500, 1819, 181, 819, 819, 1950, 50, 950, 950, 1981, 19, 981, 981, 1991, 9, 991, 991, 1995, 5, 995, 995, 1999, 1, 999, 999, 15000, 5000, 5000, 5000, 18182, 1818, 8182, 8182

Offset: 1

Author

Eric Angelini and Tom Duff, Feb 26 2020

Keywords

• base
• nonn

Comments

The sequence is infinite as one can always multiply a(4n+1) by 10 and do the same with the next three terms. It is conjectured that at least two of those three terms must be equal.

Examples

			For n = 0, we have a(4n+1) = a(1) = 15 and 15 is the sum 5 + 5 + 5, those last three terms being a(2), a(3), a(4) and substrings of a(1);
For n = 3, we have a(4n+1) = a(13) = 182 and 182 is the sum 18 + 82 + 82, those last three terms being a(14), a(15), a(16) and substrings of a(13).
		

Links

• Éric Angelini, post to Math-Fun