[seqfan] proposals

[Mason John]

Dear Seqfans
I will publish these sequences if they are considered interesting.

1. a(n) = number of occurrences of the decimal representation of n  in the concatenation of all terms preceding a(n), or n there are no such occurrences. Clarification: define the number of occurrences of string s in string t to be the number of positions within t that have a perfect match with the digits in s. Thus the number of occurrences of 11 in 1111 is 3 and not 2.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 1, 24, 25, 26, 27, 28, 29, 30, 1, 32, 33, 1, 35, 36, 37, 38, 39, 40, 1, 1, 43, 44, 1, 46, 47, 48, 49, 50, 1, 1, 1, 54, 55, 1, 57, 58, 59, 60, 1, 1, 1, 1, 65, 66, 1, 68, 69, 70, 1, 1, 1, 1, 1, 76, 77, 1, 79, 80, 1, 1, 1, 1, 1, 1, 87, 88, 1, 90, 1, 1, 1, 1, 1, 1, 1, 1, 99, 100, 1, 102, 103, 104, 105, 106, 107, 108, 109, 1, 18

2. Lexicographically least infinite sequence of positive integers such that no term, in its decimal representation, is a substring of any other term of the sequence.

1, 2, 3, 4, 5, 6, 7, 8, 99, 909, 9009, 900009, 9000009<tel:9000009>, 90000009<tel:90000009>, 900000009<tel:900000009>

3. Lexicographically least infinite sequence of positive integers such that no term, in its decimal representation, has more than one occurrence in the string formed by the concatenation all the terms of the sequence.

1, 2, 3, 4, 5, 6, 7, 8, 909, 9009, 900009, 9000009<tel:9000009>, 90000009<tel:90000009>, 900000009<tel:900000009>

John