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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A300849 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

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Last modified August 4 15:50 EDT 2020. Contains 336202 sequences. (Running on oeis4.)