A230429 Triangle T(n,k) giving the largest member of "the infinite trunk of factorial beanstalk" (A219666) whose factorial base representation contains n digits (A084558) and the most significant such digit (A099563) is k.

1, 2, 5, 10, 17, 23, 46, 70, 92, 119, 238, 358, 476, 597, 719, 1438, 2158, 2876, 3597, 4319, 5039, 10078, 15118, 20156, 25197, 30239, 35279, 40319, 80638, 120958, 161276, 201597, 241919, 282239, 322558, 362879, 725758, 1088638, 1451516, 1814397, 2177279, 2540159, 2903038, 3265912, 3628799

Offset: 1

Author

Antti Karttunen, Oct 18 2013

Keywords

• nonn
• base
• tabl

Comments

See A007623 for the factorial number system representation.

Examples

			The first rows of this triangular table are:
1;
2, 5;
10, 17, 23;
46, 70, 92, 119;
238, 358, 476, 597, 719;
...
T(3,1) = 10 as 10 has factorial base representation 120, which is the largest such three digit term in A219666 beginning with factorial base digit 1 (in other words, for which A084558(x)=3 and A099563(x)=1).
T(3,2) = 17 as 17 has factorial base representation 221, which is the largest such three digit term in A219666 beginning with factorial base digit 2.
T(3,3) = 23 as 23 has factorial base representation 321, which is the largest such three digit term in A219666 beginning with factorial base digit 3.
		

Crossrefs

Subset of A219666. Corresponding smallest terms: A230428. Can be used to compute A230420. Right edge: A033312.

Programs

Scheme

(define (A230429 n) (if (= (A002024 n) (A002260 n)) (- (A000142 (+ (A002024 n) 1)) 1) (A219651 (A230428 (+ 1 n)))))