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A300017 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 3. 1
3, 10, 17, 1, 2, 4, 6, 20, 30, 37, 5, 8, 40, 47, 7, 16, 48, 9, 11, 12, 13, 14, 15, 18, 38, 22, 50, 27, 23, 60, 19, 21, 70, 80, 28, 32, 67, 33, 68, 42, 57, 43, 58, 52, 24, 25, 26, 29, 36, 90, 100, 110, 107, 53, 49, 31, 69, 41, 59, 51, 54, 46, 34, 35, 39, 44, 78, 117, 63, 45, 55, 120, 87, 56, 61 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence starts with a(1) = 3 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

3 shows a digit 3, of course (k = 1)

3 + 10 = 13 and 13 shows at least a digit 3 (k = 2)

3 + 10 + 17 = 30 and 30 shows at least a digit 3 (k = 3)

3 + 10 + 17 + 1 = 31 and 31 shows at least a digit 3 (k = 4)

3 + 10 + 17 + 1 + 2 = 33 and 33 shows at least a digit 3 (k = 5)

3 + 10 + 17 + 1 + 2 + 4 = 37 and 37 shows at least a digit 3 (k = 6)

...

CROSSREFS

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

Sequence in context: A141497 A059911 A160375 * A176760 A188396 A190763

Adjacent sequences:  A300014 A300015 A300016 * A300018 A300019 A300020

KEYWORD

nonn,base

AUTHOR

Eric Angelini and Jean-Marc Falcoz, Feb 23 2018

STATUS

approved

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Last modified March 26 12:43 EDT 2019. Contains 321497 sequences. (Running on oeis4.)