A276949 Index of row where n is located in array A276953 (equally: column in A276955).

0, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5

Offset

0,3

Comments

This is the smallest difference that occurs between any nonzero digit's radix (which is one more than its one-based position from the right) and that digit's value in the factorial base representation of n. See A225901 and the example.

a(0) = 0 by convention, as there are no nonzero digits present, and neither does 0 occur in arrays A276953 & A276955.

Links

Antti Karttunen, Table of n, a(n) for n = 0..5040

Index entries for sequences related to factorial base representation

Formula

a(0) = 0, and for n >= 1: if A276950(n) = 1, then a(n) = 1, otherwise a(n) = 1 + a(A266193(n)).

Other identities. For all n >= 0:

a(n) = A257679(A225901(n)) = A257679(A275847(n)) = A257679(A273667(n)).

Example

For n=8, its factorial base representation (A007623) is "110", where the radix for each digit position 1, 2, 3 (from the right) is 2, 3, 4 (one larger than the position). For the 1 in the middle position the difference is 3-1 = 2, while for the 1 at the left we obtain 4-1 = 3. Of these two differences 2 is smaller, thus a(8)=2.

Prog

(Scheme, two alternative implementations)
(definec (A276949 n) (cond ((zero? n) n) ((= 1 (A276950 n)) 1) (else (+ 1 (A276949 (A266193 n))))))
(define (A276949 n) (A257679 (A225901 n)))

Crossrefs

Cf. A007623, A257679, A266193, A276950.

Cf. A276951 (for the other index).

Cf. arrays A276953 & A276955.

Cf. also A225901, A273667, A275847.

Sequence in context: A102054 A111604 A101491 * A205794 A241665 A175307

Adjacent sequences: A276946 A276947 A276948 * A276950 A276951 A276952

Keyword

nonn,base

Author

Antti Karttunen, Sep 22 2016

Status

approved