cp's OEIS Frontend

A172005 Shortest SNUSP representation of a number using only + and @.

%I A172005 #5 Jun 01 2025 21:44:03
%S A172005 1,2,3,4,4,5,5,5,6,7,6,7,6,7,7,8,7,7,8,8,7,8,8,9,9,8,8,8,8,9,9,10,9,8,
%T A172005 9,10,9,9,10,11,9,10,9,10,9,10,9,10,11,11,11,12,10,11,9,10,10,10,10,
%U A172005 10,10,11,11,12,10,11,11,10,10,11,11,12,10,11,11,10,11,11,12,11,12,13,11,12
%N A172005 Shortest SNUSP representation of a number using only + and @.
%C A172005 SNUSP is a programming language where each command is an individual letter. The two 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.
%C A172005 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 is a minimal string of these characters. The i-th element of the sequence gives the minimal number of characters (excluding the "#" which is always the last character) to produce an SNUSP program which sets the data to i. The string above is a minimal string to produce 5 and have four characters before the # so the 5th item in the sequence is 4.
%C A172005 All sequences for values >= 3 end in @++ or +++, both of which are equivalent so there are an even number of sequences for every value, half of which end in +++ and half of which end in @++. There are several variations to this sequence which I'll also enter in. They include allowing "-" to decrement the data, the number of minimal sequences and numbers which require a "-" in their minimal expression.
%H A172005 <a href="http://www.esolangs.org/wiki/SNUSP">SNUSP - Esolang</a>
%H A172005 <a href="http://c2.com/cgi/wiki?SnuspLanguage">Snusp Language</a>
%e A172005 To produce 10, there are 4 minimal sequences, each of length 7 (as always, excluding the #): +@+++++# ++@@+++# +@++@++# ++@@@++# Thus a(10)=7.
%K A172005 nonn
%O A172005 1,2
%A A172005 Darrell Plank (jar_czar(AT)msn.com), Jan 22 2010