Correspondence. [To the Editor.]

Progress, Volume III, Issue I, 1 November 1907, Page 21

Correspondence. [To the Editor.]

Sii. — Some of your readers who are fond of figures may find the following matter interesting. I lately read in ai American paper that some mathematician had announced the curious persistency, under multiplication, of the figures 142857, thus :—: — 142857 142857 142857 2 3 4 285714 42857 1 57 1 42§ 142857 142857 5 6 714285 8571^2 The way in which the figures follow each other seems undisturbed, till multiplying by seven we get the extraordinary departure :—: — 142857 7 999999 Here, so far as my information went, the matter ended, apparently with the idea that the series was exhausted. Out of curosity I carried it further :—: — 142857 142857 8 9 1142856 1285713 Now, in these we have in each one figure too man} T to compare with the original number, but if we add it in we get the same series, viz., 1142856 — 6 plus I=7 so 142857; 1285713 — Spins I=4, so 285714. Of course 142857^/510= 1428570 and the series begins again with outside figures added Multiplied by 35, or any other multiple of seven, the result is always in the 9 series, viz., 499995 the 5 and 4 end figures making the full 9. — Yours faithfully, Fdw. Tregfar. Wellington, 4/10/07