A265891 a(n) = A099563(A000407(n)); the most significant digit in factorial base representation of (2n+1)! / n!.

1, 1, 2, 1, 3, 8, 2, 6, 1, 3, 10, 1, 5, 14, 1, 5, 16, 1, 5, 15, 1, 4, 12, 1, 3, 9, 28, 2, 6, 19, 1, 3, 11, 35, 2, 6, 19, 1, 3, 10, 30, 1, 4, 14, 44, 2, 6, 20, 61, 2, 8, 25, 1, 3, 10, 31, 1, 3, 11, 35, 1, 4, 12, 38, 1, 4, 12, 39, 1, 4, 12, 39, 1, 3, 11, 36, 1, 3, 10, 33, 102, 3, 9, 28, 89, 2, 7, 23, 74, 1, 6, 19, 59

Offset: 0

Author

Antti Karttunen, Dec 20 2015

Keywords

• nonn
• base
• look

Examples

			The terms A000407(0) .. A000407(8) in factorial base representation (A007623) look as:
  1, 100, 2200, 110000, 3000000, 82000000, 2374000000, 65500000000, 1550000000000, ...
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, 3, 8, 2, 6, 1, ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10080
• Antti Karttunen, Scatter-plot of the graph drawn for the terms n=0 .. 1024, with the help of OEIS-plot utility.
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A000407, A007623, A099563.

Main diagonal of A265890 (apart from the corner term).

Cf. A265897 (positions of ones).

Cf. also A265894.

Programs

Mathematica

a[n_] := Module[{k = (2*n+1)!/n!, m = 2, r, d=0}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, If[r > 0, d = r]; m++]; d]; Array[a, 100, 0] (* Amiram Eldar, Feb 14 2024 *)

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); };
A265891 = n -> A099563(((2*n)+1)! / n!);

Scheme

(define (A265891 n) (A099563 (A000407 n)))

Scheme

(define (A265891 n) (A265890bi (+ 1 n) (+ 1 n))) ;; Code for A265890bi given in A265890.

Formula

a(n) = A099563(A000407(n)).

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