

A113880


Variation on Recamán's sequence utilizing the four basic operations (/  + *) in that order.


0



1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 432, 407, 381, 354, 326, 297, 267, 236, 204, 171, 137, 102, 66, 29, 67, 28, 68, 27, 69, 26, 70, 115, 161, 114, 162, 113, 163, 112, 60, 3180, 3126, 3071, 3015, 2958, 51, 110, 50, 111, 49
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OFFSET

1,2


COMMENTS

More precisely:
a(n) = a(n1)/n if a(n1)/n is integer and not already in the sequence. Else:
a(n) = a(n1)n if a(n1)n is positive and not already in the sequence. Else:
a(n) = a(n1)+n if a(n1)+n is not already in the sequence. Else:
a(n) = a(n1)*n if a(n1)*n is not already in the sequence. Else STOP.
In other words, divide if you can, else subtract, else add, else multiply.
By a(1000) there are 3 division steps, 928 subtraction steps, 59 addition steps and 10 multiplication steps. It is unlikely that every number belongs to the sequence since there are many "holes". It is an open question if there are any repetitions after a multiplication step. Can anybody expand the series?


LINKS

Table of n, a(n) for n=1..62.


EXAMPLE

a(24)=432 because: a(23) = 18.
18/24 is not an integer.
1824 is negative.
18 + 24 = 42 is already in the sequence
Therefore 18 * 24 = 432.


CROSSREFS

Cf. A005132.
Sequence in context: A064387 A064389 A118201 * A171884 A226940 A098141
Adjacent sequences: A113877 A113878 A113879 * A113881 A113882 A113883


KEYWORD

nonn


AUTHOR

Sergio Pimentel, Jan 27 2006


STATUS

approved



