cp's OEIS Frontend

A376002 Positions of records in A032662.

%I A376002 #9 Sep 06 2024 20:17:45
%S A376002 1,3,5,22,84,99,511,803,9999,18887,1378751,103974046
%N A376002 Positions of records in A032662.
%C A376002 Numbers k such that the first j for which the concatenation j || j+k is prime is greater than for any previous k.
%C A376002 In order for j || j+k to be prime where j+k has d digits, k and 10^d+1 must be coprime.
%e A376002 a(5) = 84 because A032662(84) = 929 which is greater than A032662(k) for all k < 84.
%p A376002 tcat:= (a,b) -> a*10^(1+ilog10(b))+b:
%p A376002 f:= proc(n) local k,k0,d;
%p A376002   for d from ilog10(n)+1 do
%p A376002     if igcd(10^d+1,n) = 1 then
%p A376002       k0:= max(1,10^(d-1)-n);
%p A376002       if (k0+n)::even then k0:= k0+1 fi;
%p A376002       for k from k0 to 10^d-n-1 by 2 do
%p A376002         if isprime(tcat(k,k+n)) then return k fi
%p A376002    od fi od
%p A376002 end proc:
%p A376002 R:= NULL: m:= 0: count:= 0:
%p A376002 for i from 1 while count < 11 do
%p A376002   v:= f(i);
%p A376002   if v > m then
%p A376002     count:= count+1; m:= v; R:= R,i;
%p A376002   fi;
%p A376002 od:
%p A376002 R;
%Y A376002 Cf. A032662, A376006.
%K A376002 nonn,base,more
%O A376002 1,2
%A A376002 _Robert Israel_, Sep 05 2024