A227187 Numbers n whose factorial base representation A007623(n) contains at least one nonleading zero. (Zero is also included as a(0)).

0, 2, 4, 6, 7, 8, 10, 12, 13, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 40, 42, 43, 44, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 60, 61, 62, 64, 66, 67, 68, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 84, 85, 86, 88, 90, 91

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..10000

Index entries for sequences related to factorial base representation.

Formula

a(0) = 0, a(1) = 2, and for n > 1, if a(n-1) is odd or A257510(a(n-1)) > 1, then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1) + 2. - Antti Karttunen, Apr 29 2015

Other identities:

For all n >= 2, a(A132371(n)) = A000142(n) = n! [See comments in A227157.]

Mathematica

q[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; MemberQ[s, 0]]; q[0] = True; Select[Range[0, 100], q] (* Amiram Eldar, Feb 07 2024 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A227187 (ZERO-POS 0 0 A208575))
(definec (A227187 n) (if (<= n 1) (+ n n) (let ((prev (A227187 (- n 1)))) (cond ((odd? prev) (+ 1 prev)) ((> (A257510 prev) 1) (+ 1 prev)) (else (+ 2 prev))))))

Crossrefs

Complement: A227157.

The sequence gives all positions n where A208575 is zero and all terms where A257510 (also A257260) are nonzeros.

Cf. A232745 (a subsequence), A232744.

Cf. also A007623, A132371, A153880, A227130, A227132, A256450 (numbers with at least one 1 in their factorial representation).

Sequence in context: A153347 A330945 A153167 * A047237 A285520 A039028

Adjacent sequences: A227184 A227185 A227186 * A227188 A227189 A227190

Keyword

nonn,base

Author

Antti Karttunen, Jul 04 2013

Status

approved