# hakmem 56 cont

N. J. A. Sloane njas at research.att.com
Fri Nov 20 22:54:53 CET 1998

```John, yes, you are right:

%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.

no doubt the authors of hakmem 56 will clarify things

also, it would be nice to have more terms for the second column,

also more terms of the sequence 0, 77, 769, ... giving the smallest
n-digit number with the max persistence of any n-digit number,

also of this one:

%S A046148 10,1,9,12,20
%N A046148 a(n) is the number of n-digit numbers with maximal multiplicative persistence A14553
%R A046148
%Y A046148 Cf. A014553,A046149,A046150.
%A A046148 Eric W. Weisstein (eww6n at virginia.edu)

and also

%I A046149
%S A046149 0,77,679,6788,68889
%N A046149 a(n) is the smallest n-digit number with maximal multiplicative persistence A14553
%R A046149
%Y A046149 Cf. A014553,A046148,A046150.
%A A046149 Eric W. Weisstein (eww6n at virginia.edu)
%O A046149 1,2
%K A046149 nonn,more

%I A046150
%S A046150 9,77,976,8876,98886
%N A046150 a(n) is the largest n-digit number with maximal multiplicative persistence A14553
%R A046150
%Y A046150 Cf. A014553,A046148,A046149.
%A A046150 Eric W. Weisstein (eww6n at virginia.edu)
%O A046150 1,1
%K A046150 nonn,more

I will copy to the seq-fan mailing list; apologies for
the overlaps

NJAS

```