%I #14 Aug 09 2022 14:13:25
%S 2,3,5,7,19,29,37,47,59,79,89,199,269,359,379,389,479,499,599,797,887,
%T 997,1889,1999,2689,2699,2789,2999,3889,3989,4789,4799,4889,4999,6899,
%U 8999,25999,27799,28789,28979,29989,37799,37889,39799,39989,48799,48889
%N Primes related to the strictly increasing subsequence of A053666.
%C a(1)=2; a(n+1) is the smallest prime with product of digits > product of digits of a(n).
%C From _Wolfdieter Lang_, Oct 31 2014: (Start)
%C A053666 is sieved as follows:
%C 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%C 2, 3, 5, 7, 1, 3, 7, 9, 6, 18, 3, 21, 4, 12, 28, ...
%C 2, 3, 5, 7, x, x, x, 9, x, 18, x, 21, x, x, 28,
%C and the related primes are:
%C 2, 3, 5, 7, 19, 29, 37, 47, ...
%C (End)
%C 
%H Shyam Sunder Gupta, <a href="/A230041/b230041.txt">Table of n, a(n) for n = 1..142</a>
%e a(6) = 29, product of digits is 18; a(7) = 37, product of digits is 21 and 21 > 18.
%t a = {}; t = 0; Do[s = Apply[Times, IntegerDigits[Prime[n]]]; If[s > t, t = s; AppendTo[a, Prime[n]]], {n, 1, 10^4}]; a
%Y Cf. A000040, A069802, A053666.
%K nonn,base,easy
%O 1,1
%A _Shyam Sunder Gupta_, Oct 06 2013
%E Edited. Name specified. A000040, A053666 and 'easy' added by _Wolfdieter Lang_, Oct 31 2014
