A300021 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 7.

7, 10, 20, 30, 3, 1, 2, 4, 40, 50, 5, 6, 9, 60, 23, 8, 19, 70, 11, 29, 63, 17, 80, 12, 18, 73, 27, 13, 14, 15, 16, 21, 22, 39, 33, 37, 64, 26, 74, 36, 65, 25, 75, 35, 66, 24, 76, 34, 67, 43, 53, 31, 28, 32, 38, 48, 90, 41, 49, 44, 46, 54, 56, 45, 55, 47, 83, 100, 110, 42, 51, 57, 58, 52, 120, 123, 77, 124, 86, 113, 87, 59, 61, 93, 97, 103, 101, 96, 104, 99, 102

Offset

1,1

Comments

The sequence starts with a(1) = 7 and is always extended with the smallest integer not yet present that does not lead to a contradiction.

A permutation of the natural numbers.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Example

7 shows a digit 7, of course (k = 1)
7 + 10 = 17 and 17 shows at least a digit 7 (k = 2)
7 + 10 + 20 = 37 and 37 shows at least a digit 7 (k = 3)
7 + 10 + 20 + 30 = 67 and 67 shows at least a digit 7 (k = 4)
7 + 10 + 20 + 30 + 3 = 70 and 70 shows at least a digit 7 (k = 5)
7 + 10 + 20 + 30 + 3 + 1 = 71 and 71 shows at least a digit 7 (k = 6)
...

Crossrefs

Cf. A300015 (which is the lexicographic first sequence of positive integers without duplicate terms having this property).

Sequence in context: A240791 A064210 A249942 * A363292 A327977 A097634

Adjacent sequences: A300018 A300019 A300020 * A300022 A300023 A300024

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Feb 23 2018

Status

approved