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%I #7 Dec 23 2018 23:29:34
%S 1,2,3,4,4,5,5,5,6,7,6,7,6,7,7,8,7,7,8,8,7,8,8,9,8,8,8,8,8,9,9,9,9,8,
%T 9,10,9,9,10,10,9,10,9,10,9,10,9,10,10,10,10,10,10,10,9,10,10,10,10,
%U 10,10,10,11,11,10,11,10,10,10,11,11,11,10,11,11,10,11,11,11,11,11,11,11,12
%N Shortest SNUSP representation of a number using only +, - and @
%C SNUSP is a programming language where each command is an individual letter. The four of concern here are +, -, @ and #. + increments the current data value, - decrements it, @ 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 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 has four characters before the # so the 5th item in the sequence is 4.
%C Sequence A172005 is the same as this one but disallows the '-' command. Many values have smaller sequences by allowing the -. There are some sequences that can cut up to two characters off by using the -. I don't know if larger savings are possible or if the savings can become arbitrarily large.
%H <a href="http://www.esolangs.org/wiki/SNUSP">SNUSP - Esolang</a>
%H <a href="http://c2.com/cgi/wiki?SnuspLanguage">SNUSP Language</a>
%e To produce 10, there are 4 minimal sequences, each of length 7 (as always, excluding the #): +@+++++# ++@@+++# +@++@++# ++@@@++# Thus a(10)=7. The first value that requires a - in its minimal representation is 25 which requires 8 characters. If we disallow the '-' command (as in sequence A172005), it requires 9 characters.
%p See A172005.
%Y Cf. A172005.
%K nonn
%O 1,2
%A Darrell Plank (jar_czar(AT)msn.com), Jan 22 2010
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