A376002 - OEIS

%I #9 Sep 06 2024 20:17:45

%S 1,3,5,22,84,99,511,803,9999,18887,1378751,103974046

%N Positions of records in A032662.

%C Numbers k such that the first j for which the concatenation j || j+k is prime is greater than for any previous k.

%C In order for j || j+k to be prime where j+k has d digits, k and 10^d+1 must be coprime.

%e a(5) = 84 because A032662(84) = 929 which is greater than A032662(k) for all k < 84.

%p tcat:= (a,b) -> a*10^(1+ilog10(b))+b:

%p f:= proc(n) local k,k0,d;

%p   for d from ilog10(n)+1 do

%p     if igcd(10^d+1,n) = 1 then

%p       k0:= max(1,10^(d-1)-n);

%p       if (k0+n)::even then k0:= k0+1 fi;

%p       for k from k0 to 10^d-n-1 by 2 do

%p         if isprime(tcat(k,k+n)) then return k fi

%p    od fi od

%p end proc:

%p R:= NULL: m:= 0: count:= 0:

%p for i from 1 while count < 11 do

%p   v:= f(i);

%p   if v > m then

%p     count:= count+1; m:= v; R:= R,i;

%p   fi;

%p od:

%p R;

%Y Cf. A032662, A376006.

%K nonn,base,more

%O 1,2

%A _Robert Israel_, Sep 05 2024