

A172008


Count of minimal SNUSP programs using +, @ and # to yield N


1



1, 1, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 2, 4, 2, 2, 4, 2, 6, 2, 2, 2, 8, 8, 4, 2, 2, 2, 2, 2, 2, 6, 2, 2, 10, 10, 4, 2, 8, 8, 2, 2, 4, 8, 2, 2, 2, 6, 14, 2, 4, 4, 8, 8, 2, 4, 2, 4, 2, 2, 2, 4, 6, 6, 2, 2, 2, 2, 4, 4, 18, 18, 2, 2, 4, 2, 8, 2, 10, 2, 2, 2, 4, 4, 6, 4, 4, 4, 2, 2, 2, 4, 6, 6, 2, 2, 2, 8, 2, 2, 6, 6, 2
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OFFSET

1,3


COMMENTS

Shortest SNUSP representation of a number using only + and @ is in A172005.
SNUSP is a programming language where each command is an individual letter. The three of concern here are + and @ and #. + increments the current data value, @ is a "subroutine call" and # is a "return". When an @ is encountered, a record of the location is put on a stack and execution continues. When a # is encountered, if there is a return point on the stack, the execution continues at that a single character beyond that return point. If there is no return point on the stack, execution terminates.
Thus "@@++#" would put the first two "@" return points on the stack, increment data twice, return from the second "@" to the last "+", increment the data once more, return from the first "@" to the first "+", increment the data two more times and finally terminate when it hits the "#" with no return points on the stack. The data is always initialized to zero so this effectively puts 5 into the data. In order to place a particular value into the data, there one or more minimal strings of these characters. The i'th element of the sequence gives the number of minimal SNUSP programs using only these characters. After 2, all sequences end in either +++ or @++ both of which are equivalent so that all values above a(2) are even.


LINKS

Table of n, a(n) for n=1..103.
SNUSP  Esolang
SNUSP Language


EXAMPLE

19 can be represented minimally in 6 ways using @, + and #: @+@+++++# +@@@++++# @++@@+++# @+@++@++# +@@@+@++# @++@@@++# Thus a(19) = 6.


MAPLE

See A172005


CROSSREFS

A172005, A172006, A172007
Sequence in context: A268045 A118177 A105069 * A100825 A216452 A307616
Adjacent sequences: A172005 A172006 A172007 * A172009 A172010 A172011


KEYWORD

nonn


AUTHOR

Darrell Plank (jar_czar(AT)msn.com), Jan 22 2010


STATUS

approved



