



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

0,3


COMMENTS

After zero, a(n) = number of positions where digits in the factorial base representations of successive nodes A219666(n1) and A219666(n) in the infinite trunk of the factorial beanstalk differ from each other.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..3149


FORMULA

a(0)=0, and for n>=1, a(n) = A230415(A219666(n),A219666(n1)).
For all n, a(A226061(n+1)) = A232094(n).


EXAMPLE

a(8) = 1, because A219666(8)=23, whose factorial base representation (A007623(23)) is '321', and A219666(7)=17, whose factorial base representation (A007623(17)) is '221', and they differ just in one digit position.
a(9) = 3, because A219666(9)=25, '...01001' in factorial base, which differs from '...0321' in three digit positions.
Note that A226061(4)=8 (A226061(n) tells the position of (n!)1 in A219666), and 1+2+3 = 6 happens to be both a triangular number (A000217) and a factorial number (A000142).
The next time 1 occurs in this sequence because of this coincidence is at x=A226061(16) (whose value is currently not known), as at that point A219666(x) = 16!1 = 20922789887999, whose factorial base representation is (15,14,13,12,11,10,9,8,7,6,5,4,3,2,1), and A000217(15) = 120 = A000142(5), which means that A219666(x1) = A219651(20922789887999) = 20922789887879, whose factorial base representation is (15,14,13,12,11,10,9,8,7,6,4,4,3,2,1), which differs only in one position from the previous.
Of course 1's occur in this sequence for other reasons as well.


MATHEMATICA

nn = 1200; m = 1; While[m! < nn, m++]; m; f[n_] := IntegerDigits[n, MixedRadix[Reverse@ Range[2, m]]]; Join[{0}, Function[w, Count[Subtract @@ Map[PadLeft[#, Max@ Map[Length, w]] &, w], k_ /; k != 0]]@ Map[f@ # &, {#1, #2}] & @@@ Partition[#, 2, 1] &@ TakeWhile[Reverse@ NestWhileList[#  Total@ f@ # &, nn, # > 0 &], # <= 500 &]] (* Michael De Vlieger, Jun 27 2016, Version 10 *)


PROG

(Scheme)
(define (A230410 n) (if (zero? n) n (A230415bi (A219666 n) (A219666 ( n 1))))) ;; Where bivariate function A230415bi has been given in A230415.


CROSSREFS

Cf. A230415, A230406, A231717, A231719, A232094. A230422 gives the positions of ones.
Sequence in context: A306459 A297788 A194342 * A044925 A323356 A319244
Adjacent sequences: A230407 A230408 A230409 * A230411 A230412 A230413


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Nov 10 2013


STATUS

approved



