Matchstick numbers

NAME#1

Integers A that cannot produce an integer B > A by moving a single matchstick. See the Comment and Example sections for more details.

DATA#1

1, 5, 7, 8, 9, 11, 15, 51, 55, 71, 75, 77, 78, 79, 87, 88, 91, 95, 97, 98, 99, 111, …

COMMENT#1

The usual font used for "Matchstick" numbers is illustrated there: https://oeis.org/A126803/a126803.pdf

EXAMPLE#1

We don't start the sequence with 0 — as it is possible to move one match in 0 to form 6 or 9, which are both bigger than 0.

We start the sequence with a(1) = 1 as moving one match from 1 cannot produce another digit.

We cannot have a(2) = 2 as we can move one match of 2 to get 3; we cannot have a(2) = 3 as we can move one match of 3 to get 5; we cannot have a(2) = 4 as we can move one match from 4 to get 11;

We have a(2) = 5 as we cannot produce an integer > 5 by moving exactly one match in 5 (we can produce 3, but 3 < 5).

We don't have a(8) = 17 as 17 can form 71 by moving the horizontal match (though the space between the 7 and the 1 is large). Likewise the integer 57 is not in the sequence because we can move the horizontal match of 7 to transform the digit 5 into 6 or 9; in both cases 57 is smaller than its transform.

We don't have a(15) = 81 as 81 can form 97 by moving a single match (though the space between the 9 and the 7 may look as inexistent: just consider that the two digits of 81 were separated by more than the size of an horizontal match).

NAME#2

The successive nonnegative numbers, transformed into the largest possible integer by moving a single matchstick . See the Comment and Example sections for more details..

DATA#2

9, -1, 3, 5, 11, 3, 9, -1, -1, 6, 19, 4, 13, 15, 111, 13, 75, 71, 79, 75, ...

COMMENT#2

The usual font used for "Matchstick" numbers is the one illustrated here: https://oeis.org/A126803/a126803.pdf

We put -1 when no transformation is possible for n.

EXAMPLE#2

n = 0 becomes 5 or 9 by moving a single match; we keep 9 as 9 is larger than 6;

n = 1 cannot be transformed in anything, producing thus -1 in the sequence;

n = 2 becomes 3 by moving a single match;

n = 3 becomes 5 by moving a single match;

n= 4 becomes 11 by moving a single match; etc.

(another matchstick seq)

(the font we like the most for this kind of exercise)