A265899 -id:A265899 - cp's OEIS frontend

A266120 Local maxima of A265894 just before its descents: a(n) = A265894(A265899(n) - 1).

1, 2, 6, 4, 7, 10, 11, 10, 25, 19, 38, 23, 39, 20, 29, 40, 51, 62, 70, 77, 79, 78, 73, 66, 57, 47, 118, 91, 68, 49, 106, 71, 147, 93, 57, 108, 62, 112, 61, 105, 174, 89, 141, 68, 104, 154, 224, 100, 139, 191, 80, 105, 136, 172, 215, 263, 98, 116, 135, 154, 174, 192, 210, 225, 238, 248, 254, 257, 256, 251, 244, 233, 219, 204, 187, 169, 151, 133

Offset: 1

Antti Karttunen, Dec 24 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..2016

Cf. A265894, A265899.

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!);
i=0; p=1; n=0; while(i < 2016, n++; k = A265894(n); if(k <= p, i++; write("b266120.txt", i, " ", p)); p = k; );

(define (A266120 n) (A265894 (- (A265899 n) 1)))

a(n) = A265894(A265899(n) - 1).

A266119 First differences of A265899.

Original entry on oeis.org

2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 5, 4, 4, 5, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 6, 5, 6, 5, 5, 6, 5, 6, 5, 6, 5, 6, 5

Offset: 1

Antti Karttunen, Dec 24 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..1502

Cf. A265899.

(define (A266119 n) (- (A265899 (+ 1 n)) (A265899 n)))

a(n) = A265899(n+1) - A265899(n).

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

Original entry on oeis.org

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

Antti Karttunen, Dec 24 2015

			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, ...

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

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.

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 *)

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!);

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

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

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

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

A265898 Numbers n for which (2n)! / n! [= A001813(n)] is >= k! but < 2*k! for some k; positions of ones in A265894.

Original entry on oeis.org

0, 1, 3, 6, 8, 11, 14, 17, 20, 27, 34, 41, 45, 49, 81, 85, 89, 102, 106, 115, 124, 128, 137, 142, 146, 151, 160, 169, 174, 188, 193, 202, 207, 212, 231, 236, 241, 246, 251, 256, 306, 311, 316, 321, 326, 331, 336, 357, 362, 367, 383, 388, 393, 409, 414, 425, 430, 446, 462, 478, 489, 494, 505, 516, 521, 532, 543, 554, 565

Offset: 0

Antti Karttunen, Dec 24 2015

nonn

a(0) = 0 is a special case in this sequence, thus the indexing starts from zero.

Numbers n such that A001813(n) is in A265334.

Antti Karttunen, Table of n, a(n) for n = 0..843

After zero-term, a subsequence of A265899.
Cf. A001813, A265894, A265334.
Cf. also A265897.

cp's OEIS Frontend

A266120 Local maxima of A265894 just before its descents: a(n) = A265894(A265899(n) - 1).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Scheme

Formula

A266119 First differences of A265899.

Views

Author

Keywords

Links

Crossrefs

Programs

Scheme

Formula

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Scheme

Scheme

Formula

A265898 Numbers n for which (2n)! / n! [= A001813(n)] is >= k! but < 2*k! for some k; positions of ones in A265894.

Views

Author

Keywords

Comments

Links

Crossrefs