A265894 a(n) = A099563(A001813(n)); the most significant digit in factorial base representation of (2n)! / n!.

1, 1, 2, 1, 2, 6, 1, 4, 1, 2, 7, 1, 3, 10, 1, 3, 11, 1, 3, 10, 1, 3, 8, 25, 2, 6, 19, 1, 4, 13, 38, 2, 7, 23, 1, 4, 13, 39, 2, 6, 20, 1, 3, 9, 29, 1, 4, 13, 40, 1, 5, 16, 51, 2, 6, 20, 62, 2, 7, 23, 70, 2, 8, 25, 77, 2, 8, 25, 79, 2, 8, 25, 78, 2, 7, 23, 73, 2, 6, 21, 66, 1, 6, 18, 57, 1, 4, 15, 47, 1, 3, 12, 38, 118, 3, 9

Offset: 0

Author

Antti Karttunen, Dec 24 2015

Keywords

• nonn
• base
• look

Examples

			The terms A001813(0) .. A001813(8) in factorial base representation (A007623) look as:
  1, 10, 200, 10000, 220000, 6000000, 174000000, 4760000000, 110000000000, ...
Taking the first digit (actually: a place holder value) of each gives the terms a(0) .. a(8) of this sequence: 1, 1, 2, 1, 2, 6, 1, 4, 1, ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10080
• Index entries for sequences related to factorial base representation

Crossrefs

Submain diagonal of A265890.

Cf. A001813, A099563.

Cf. A265898 (positions of ones), A265899 (of descents), A266120 (local maxima just before those descents).

Cf. also A265891.

Programs

Mathematica

factBaseIntDs[n_] := Module[{m, i, len, dList, currDigit}, i = 1; While[n > i!, i++ ]; m = n; len = i; dList = Table[0, {len}]; Do[ currDigit = 0; While[m >= j!, m = m - j!; currDigit++ ]; dList[[len - j + 1]] = currDigit, {j, i, 1, -1}]; If[dList[[1]] == 0, dList = Drop[dList, 1]]; dList]; (* taken from A007623,  Alonso del Arte, May 03 2006 *) f[n_] := factBaseIntDs[(2 n)!/n!][[1]]; Array[f, 96, 0] (* Robert G. Wilson v, Dec 25 2015 *)

PARI

allocatemem((2^31)); \\ Enough?
A099563(n) = { my(i=2,dig=0); until(0==n, dig = n % i; n = (n - dig)/i; i++); return(dig); };
A265894 = n -> A099563((2*n)! / n!);

Scheme

(define (A265894 n) (A099563 (A001813 n)))

Scheme

(define (A265894 n) (A265890bi (+ 1 n) n)) ;; Code for A265890bi given in A265890.

Formula

a(n) = A099563(A001813(n)).

a(n) = A265890(n+1, n).