A268517 Three-digit numbers, starting with 321, such that when written in a table with three columns, there are arithmetic progressions modulo 10 down the diagonals, with steps of 1, 2 and 3 respectively.

321, 444, 675, 680, 370, 268, 949, 206, 851, 208, 132, 444, 567, 68, 37, 826, 994, 620, 185, 820, 213, 444, 756, 806, 703, 682, 499, 62, 518, 82, 321, 444, 675, 680, 370, 268, 949, 206, 851, 208, 132, 444, 567, 68, 37, 826, 994, 620, 185, 820, 213, 444, 756, 806

Offset

0,1

Comments

Repeats after 30 terms. - Chai Wah Wu, Feb 08 2016

References

GCHQ Director's Christmas Puzzles for 2015.

Links

Table of n, a(n) for n=0..53.

GCHQ, Solutions to Director's Christmas Puzzles for 2015

Example

The table begins
3 2 1
4 4 4
6 7 5
6 8 0
3 7 0
2 6 8
9 4 9
2 0 6
8 5 1
2 0 8
...
and one can see the three arithmetic progressions down the diagonals: 3, 4, 5, 6, ...; 2, 4, 6, 8, ...; 1, 4, 7, 0, ... .

Prog

(Python)
from __future__ import division
A268517_list = [321]
for i in range(10**4):
    a = A268517_list[-1]
    A268517_list.append(((a+1+(2-i)%3) % 10)*100 + ((a//100+1+(-i)%3) % 10)*10 + ((a//10+1+(1-i)%3) % 10)) # Chai Wah Wu, Feb 08 2016

Crossrefs

Sequence in context: A351994 A261262 A308527 * A228226 A004927 A074350

Adjacent sequences: A268514 A268515 A268516 * A268518 A268519 A268520

Keyword

nonn,base

Author

N. J. A. Sloane, Feb 08 2016

Extensions

More terms from Chai Wah Wu, Feb 08 2016

Status

approved