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A230428 Triangle T(n,k) giving the smallest term in "the infinite trunk of factorial beanstalk" (A219666) whose factorial base representation contains n digits (A084558) and the most significant such digit (A099563) is k.

%I A230428 #7 Oct 19 2013 11:00:27
%S A230428 1,2,5,7,12,23,25,48,74,97,121,240,362,481,605,721,1440,2162,2881,
%T A230428 3605,4326,5041,10080,15122,20161,25205,30246,35288,40321,80640,
%U A230428 120962,161281,201605,241926,282248,322568,362881,725760,1088642,1451521,1814405,2177286,2540168,2903048,3265923
%N A230428 Triangle T(n,k) giving the smallest term in "the infinite trunk of factorial beanstalk" (A219666) whose factorial base representation contains n digits (A084558) and the most significant such digit (A099563) is k.
%e A230428 The first rows of this triangular table are:
%e A230428 1;
%e A230428 2, 5;
%e A230428 7, 12, 23;
%e A230428 25, 48, 74, 97;
%e A230428 121, 240, 362, 481, 605;
%e A230428 ...
%e A230428 T(3,1) = 7 as 7 has factorial base representation 101, which is the smallest such three digit term in A219666 beginning with factorial base digit 1 (in other words, for which A084558(x)=3 and A099563(x)=1).
%e A230428 T(3,2) = 12 as 12 has factorial base representation 200, which is the smallest such three digit term in A219666 beginning with factorial base digit 2.
%e A230428 T(3,3) = 23 as 23 has factorial base representation 321, which is the smallest such three digit term in A219666 beginning with factorial base digit 3.
%o A230428 (Scheme)
%o A230428 (define (A230428 n) (if (< n 3) n (let ((k (A002260 n))) (let loop ((i (A230429 n)) (prev_i 0)) (cond ((not (= (A099563 i) k)) prev_i) (else (loop (A219651 i) i)))))))
%Y A230428 Subset of A219666. Corresponding largest terms: A230429. Cf. also A230420.
%K A230428 nonn,base,tabl
%O A230428 1,2
%A A230428 _Antti Karttunen_, Oct 18 2013