A362075 a(1) = 1, a(2) = 2; for n > 2, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-2) + a(n-1).

1, 2, 4, 3, 5, 6, 7, 8, 9, 20, 10, 11, 30, 22, 13, 12, 14, 15, 16, 24, 17, 23, 18, 25, 19, 21, 26, 28, 27, 29, 31, 32, 40, 33, 41, 35, 34, 37, 36, 42, 39, 43, 44, 45, 46, 38, 50, 47, 48, 60, 49, 52, 53, 62, 63, 64, 54, 55, 56, 57, 58, 66, 59, 67, 70, 65, 68, 69, 80, 72, 73, 76, 75, 74, 77, 78

Offset

1,2

Comments

The sequence is likely to be finite although it contains at least 100000 terms.

Sequence is finite with 4128755 terms, since a(4128754) = 46946449 and a(4128755) = 777000707 have sum 823947156. - Michael S. Branicky, Apr 08 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Michael S. Branicky, Python program

Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.

Example

a(10) = 20 as a(8) + a(9) = 8 + 9 = 17, and 20 is the smallest unused number that does not contain the digits 1 or 7.

Prog

(Python) # see linked program that generates the full sequence

Crossrefs

Cf. A362076, A342441, A342442, A067581, A297065.

Sequence in context: A222234 A374791 A374792 * A131042 A274631 A368181

Adjacent sequences: A362072 A362073 A362074 * A362076 A362077 A362078

Keyword

nonn,base,fini

Author

Scott R. Shannon, Apr 08 2023

Status

approved