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A181521 Representation of n = sum_k b_k*(k!!) in the double-factorial base by some b_k-fold concatenation of the indices k. 1
1, 2, 3, 13, 23, 33, 133, 4, 14, 24, 34, 134, 234, 334, 5, 15, 25, 35, 135, 235, 335, 1335, 45, 145, 245, 345, 1345, 2345, 3345, 55, 155, 255, 355, 1355, 2355, 3355, 13355, 455, 1455, 2455, 3455, 13455, 23455, 33455, 555, 1555, 2555, 6, 16, 26, 36, 136, 236, 336 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The encoding of n is similar to A111095 but uses a double-factorial base A006882 to define the expansion coefficients.

The expansion coefficients b_k in n = sum_{k>=1} b_k * A006882(k) are defined "greedily" by taking the largest A006882(k) which is <=n, choosing b_k as large as possible such that b_k*A006882(k) remains <=n, subtracing b_k*A006882(k) from n to define a remainder, and recursively slicing the remainder to generate b_{k-1}, then b_{k-2} etc until the remainder reduces to zero. This produces the b_k for each n equivalent to A019513(n).

This representation A019513 is then scanned from the least to the most-significant b_k, i.e., along increasing k, and for each nonzero b_k, b_k copies of k are appended to a string representation -- starting from an empty string. This final representation is interpreted as a base-10 number a(n).

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

a(39) = 1455 because 1!!+4!!+5!!+5!! = 1+8+15+15 = 39

MAPLE

dblfactfloor := proc(n) local j ; for j from 1 do if doublefactorial(j) > n then return j-1 ; end if; end do: end proc:

dblfbase := proc(n) local nshf, L, f; nshf := n ; L := [] ; while nshf > 0 do f := dblfactfloor(nshf) ; L := [f, op(L)] ; nshf := nshf-doublefactorial(f) ; end do: L ; end proc:

read("transforms") ; A181521 := proc(n) digcatL(dblfbase(n)) ; end proc:

seq(A181521(n), n=1..70) ; # R. J. Mathar, Dec 06 2010

CROSSREFS

Cf. A111095

Sequence in context: A136260 A296932 A288054 * A133201 A215302 A103150

Adjacent sequences:  A181518 A181519 A181520 * A181522 A181523 A181524

KEYWORD

easy,nonn,base

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Oct 26 2010

STATUS

approved

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Last modified July 17 16:58 EDT 2019. Contains 325107 sequences. (Running on oeis4.)