[QUOTE=CRGreathouse;238496]Also, what is sumdigits? [url=http://oeis.org/A010888]A010888[/url]? [url=http://oeis.org/A007953]A007953[/url]? Something else?[/QUOTE]

sumdigits is a function in the thread already pointed back to by Pi's questioning.

[QUOTE=science_man_88;238497]sumdigits is a function in the thread already pointed back to by Pi's questioning.[/QUOTE]

So, neither. It's like the digital root but with sumdigits(0) = 9.

Faster code:
[code]sumdigits(n)=n=n%9;if(n,n,9)[/code]

[QUOTE=CRGreathouse;238501]So, neither. It's like the digital root but with sumdigits(0) = 9.

Faster code:
[code]sumdigits(n)=n=n%9;if(n,n,9)[/code][/QUOTE]

all i have to do is take out the return() on each to cut the time by 66% or so. and yours didn't beat mine by much on my machine ( I'll double check with multiple runs)

[CODE](12:13) gp > sumdigits1(n)=if(n%9!=0,n%9,9)
%5 = (n)->if(n%9!=0,n%9,9)
(12:15) gp > sumdigits2(n)=if(n%9!=0,return(n%9),return(9))
%6 = (n)->if(n%9!=0,return(n%9),return(9))
(12:15) gp > sumdigits3(n)=n=n%9;if(n,n,9)
%7 = (n)->n=n%9;if(n,n,9)
(12:15) gp > for(x=1,10000000,sumdigits1(x))
(12:16) gp > ##
*** last result computed in 6,172 ms.
(12:16) gp > for(x=1,10000000,sumdigits2(x))
(12:16) gp > ##
*** last result computed in 16,563 ms.
(12:16) gp > for(x=1,10000000,sumdigits3(x))
(12:17) gp > ##
*** last result computed in 15,141 ms.[/CODE]

unfortunately my first sumdigits seems most effective when added into lucaslehmers()

Interesting. I wonder what Pari is doing under the hood here.

Mine is still faster for large numbers, but I can't imagine why yours is faster for small numbers.

The optimal Pari (as opposed to GP) code is surely
[code]long
digital_root(GEN n) {
if (typ(n) != t_INT)
pari_err(typeer, "digital_root");
register long ret = smodis(n, 9);
if (ret)
return ret;
return 9;
}[/code]
and I can't guess why your version would be closer to this than mine. Maybe I'll gp2c them later and find out.

[QUOTE=science_man_88;238510]unfortunately my first sumdigits seems most effective when added into lucaslehmers()[/QUOTE]

Do you need the Lucas-Lehmer residue, or just its digital root? You can compute the latter much faster.

[QUOTE=CRGreathouse;238530]Do you need the Lucas-Lehmer residue, or just its digital root? You can compute the latter much faster.[/QUOTE]

Digital root of the lucas lehmer residue ... really I didn't know that, Thanks. I'm just trying to limit it to a list of digital root 9 because we know the exponents must be in that group to work.

[QUOTE=CRGreathouse;238501]So, neither. It's like the digital root but with sumdigits(0) = 9.

Faster code:
[code]sumdigits(n)=n=n%9;if(n,n,9)[/code][/QUOTE]

what about
[code]sumdigits(n)=(n-1)%9+1[/code]?

[QUOTE=axn;238542]what about
[code]sumdigits(n)=(n-1)%9+1[/code]?[/QUOTE]

using flat out print(sumdigits(x)) it ties my fastest on my machine. I'll have to check it out on the lucas test.

[CODE](15:57) gp > for(x=1,10000000,sumdigits1(x))
(16:01) gp > ##
*** last result computed in 6,172 ms.
(16:01) gp > for(x=1,10000000,sumdigits2(x))
(16:01) gp > ##
*** last result computed in 16,891 ms.
(16:01) gp > for(x=1,10000000,sumdigits3(x))
(16:01) gp > ##
*** last result computed in 15,312 ms.
(16:01) gp > for(x=1,10000000,sumdigits4(x))
(16:02) gp > ##
*** last result computed in 5,266 ms.
(16:02) gp >[/CODE]

we have a new winner.

[CODE](16:04) gp > for(x=1,100000,lucaslehmer2(x))
3,5,7,13,17,19,23,31,33,51,61,71,89,101,107,127,139,191,271,273,305,331,347,351,367,397,405,407
*** _^s: user interrupt after 12,562 ms.
(16:04) gp > for(x=1,1000,lucaslehmer2(x))
3,5,7,13,17,19,23,31,33,51,61,71,89,101,107,127,139,191,271,273,305,331,347,351,367,397,405,407
(16:04) gp > ##
*** last result computed in 3,922 ms.
(16:04) gp > lucaslehmer2(p)= s=4;for(x=1,p-2,s=(s^2-2)%(2^p-1));if(x=p-2 && sumdigits2(s)==9,p
%21 = (p)->s=4;for(x=1,p-2,s=(s^2-2)%(2^p-1));if(x=p-2&&sumdigits2(s)==9,print1(p","))
(16:05) gp > for(x=1,1000,lucaslehmer2(x))
3,5,7,13,17,19,23,31,33,51,61,71,89,101,107,127,139,191,271,273,305,331,347,351,367,397,405,407
(16:05) gp > ##
*** last result computed in 3,953 ms.
(16:05) gp > lucaslehmer2(p)= s=4;for(x=1,p-2,s=(s^2-2)%(2^p-1));if(x=p-2 && sumdigits3(s)==9,p
%22 = (p)->s=4;for(x=1,p-2,s=(s^2-2)%(2^p-1));if(x=p-2&&sumdigits3(s)==9,print1(p","))
(16:05) gp > for(x=1,1000,lucaslehmer2(x))
3,5,7,13,17,19,23,31,33,51,61,71,89,101,107,127,139,191,271,273,305,331,347,351,367,397,405,407
(16:05) gp > ##
*** last result computed in 3,969 ms.
(16:05) gp > lucaslehmer2(p)= s=4;for(x=1,p-2,s=(s^2-2)%(2^p-1));if(x=p-2 && sumdigits4(s)==9,p
%23 = (p)->s=4;for(x=1,p-2,s=(s^2-2)%(2^p-1));if(x=p-2&&sumdigits4(s)==9,print1(p","))
(16:05) gp > for(x=1,1000,lucaslehmer2(x))
3,5,7,13,17,19,23,31,33,51,61,71,89,101,107,127,139,191,271,273,305,331,347,351,367,397,405,407
(16:05) gp > ##
*** last result computed in 4,000 ms.
(16:05) gp >[/CODE]

this is weirder and weirder lol.