persistence

N. J. A. Sloane njas at research.att.com
Sat Nov 21 03:45:57 CET 1998

```well, my article in J Rec Math is 1973, so the work
was done <= that, and hakmem is dated '72, so it's close.
but at least i published the results, and found that very nice
sequence, AND introduced the name persistence!

By the way,
the data base - as you probably noticed - contains this variant
due to David Wilson:

%I A014120
%S A014120 0,10,25,39,77,679,6788,68889,2677889,26888999,3778888999,
%T A014120 267777777889999,77777777788888888888899999,
%U A014120 37777777777777777777777777778888889999999999999999999
%N A014120 Smallest number of persistence n over product-of-nonzero-digits function.
%D A014120 N.J.A. Sloane, The persistance of a number, J. Recreational Math. 6 (1973), 97-98.
%O A014120 0,2
%K A014120 nonn,base,nice
%A A014120 David Wilson (wilson at ctron.com)
%Y A014120 Cf. A003001.

of my original

%I A003001 M4687
%S A003001 0,10,25,39,77,679,6788,68889,2677889,26888999,3778888999,
%T A003001 277777788888899
%N A003001 Smallest number of persistence n. Probably finite.
%R A003001 JRM 6 97 1973. GA91 170, 186.
%O A003001 0,2
%A A003001 njas
%P A003001 njas #33
%K A003001 nonn,fini,nice
%Y A003001 Cf. A006050, A007954, A031286, A031347, A033908, A046511, etc.
%F A003001 The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. E.g. 39->27->14->4 has persistence 3.

best regards

neil

```