OFFSET
10,2
COMMENTS
Write vertically a number (like 419) and try to win the jackpot (using the hereunder martingale):
.
(4) - a - d - g - j - m
(1) - b - e - h - k - ...
(9) - c - f - i - l - ...
.
i) compute the terms a, b, c, d, e, ... in the order shown above;
ii) the sequence a, b, c, d, e, ... is always extended with the smallest prime not occurring before, such that ...
iii) ... in each row, the first (parenthesized) digit of the next term is the rightmost digit of the preceding term;
iv) a jackpot is won when all terms in a column have the same rightmost digit.
.
4 - (4)1 - (1)3 - (3) - (3)1 - (1)01 - (1)03 - (3)07 - (7)09
1 - (1)1 - (1)7 - (7)1 - (1)9 - (9)07 - (7)01 - (1)07 - (7)19
9 - (9)7 - (7) - (7)3 - (3)7 - (7)9 - (9)11 - (1)09 - (9)19 = jackpot!
.
Indeed, we have the same digit (9) ending all the terms of the last column.
And as it takes 8 steps to win the jackpot with 419, we assign 8 to 419.
LINKS
Eric Angelini, Jackpot numbers, Jackpot numbers, personal blog.
EXAMPLE
10 => -1 (no number that contains a digit 0 can win a jackpot; we assign -1 to 10 to mark this impossibility - see the two rows generated by 10 hereunder):
1 - 11
0 - ? (no prime starts with 0)
11 => 6 steps
1 - 11 - 17 - 7 - 71 - 101 - 103
1 - 13 - 3 - 31 - 19 - 97 - 73
12 => 2 steps
1 - 11 - 13
2 - 2 - 23
13 => 3 steps
1 - 11 - 13 - 37
3 - 3 - 31 - 17
14 => 1 step
1 - 11
4 - 41
15 => 2 steps
1 - 11 - 13
5 - 5 - 53
16 => 1 step
1 - 11
6 - 61
17 => 10 steps
1 - 11 - 13 - 3 - 31 - 19 - 97 - 701 - 101 - 103 - 307
7 - 7 - 71 - 17 - 73 - 37 - 79 - 907 - 709 - 911 - 107
Etc. The number of successive steps form the sequence.
CROSSREFS
KEYWORD
sign,base
AUTHOR
Eric Angelini and Carole Dubois, Apr 24 2022
STATUS
approved