[seqfan] problems with A022920

[Richard J. Mathar]

I cannot reproduce the terms of http://oeis.org/A022920 .
Take n=8, there is the solution
7  -1 *11 -1 *13 + 1 *17 -1 *19 + 1 *23 + 1 *29 -1 *31
so a(8)=1.

Take n=10, there are the solutions
7  -1 *11 -1 *13 -1 *17 + 1 *19 + 1 *23 + 1 *29 -1 *31 + 1 *37 -1 *41;
7  -1 *11 -1 *13 + 1 *17 -1 *19 + 1 *23 -1 *29 + 1 *31 + 1 *37 -1 *41;
7  + 1 *11 -1 *13 -1 *17 -1 *19 -1 *23 + 1 *29 + 1 *31 + 1 *37 -1 *41;
7  -1 *11 -1 *13 + 1 *17 + 1 *19 -1 *23 -1 *29 + 1 *31 -1 *37 + 1 *41;
7  -1 *11 + 1 *13 -1 *17 -1 *19 + 1 *23 -1 *29 + 1 *31 -1 *37 + 1 *41;
7  -1 *11 + 1 *13 + 1 *17 -1 *19 -1 *23 -1 *29 -1 *31 + 1 *37 + 1 *41;
7  + 1 *11 -1 *13 -1 *17 + 1 *19 -1 *23 -1 *29 -1 *31 + 1 *37 + 1 *41;

so a(10)=7...
so a(12)=12...
so a(14)=61...

It a matter of taking all binary patterns with n-1 digits and checking for the 2:

# Maple
A022920 := proc(n)
        local a,b,cs,cslen ;
        a := 0 ;
        for b from 0 to 2^(n-1)-1 do
                cs := convert(b,base,2) ;
                cslen := nops(cs) ;
                if cslen < n-1 then
                        cs := [op(cs),seq(0,i=1..n-1-cslen)] ;
                end if;
                if ithprime(4)+add( (-1+2*op(i-4,cs)) *ithprime(i),i=5..n+3) = 2 then
                        printf("%d ",ithprime(4)) ;
                        for i from 5 to n+3 do
                                ci := -1+2*op(i-4,cs) ;
                                if ci > 0 then
                                        printf(" + %d *%d",ci,ithprime(i)) ;
                                else
                                        printf(" %d *%d",ci,ithprime(i)) ;
                                end if;
                        end do:
                        printf(";\n") ;
                        a := a+1 ;
                end if;
        end do:
        a ;
end proc:
for n from 1 do
        print(n,A022920(n)) ;
end do:

R. J. Mathar