A376006 Record values in A032662.

2, 4, 12, 21, 929, 938, 9500, 99204, 9990074, 99999981142, 999999998621256, 99999999999999896026031

Offset: 1

Author

Robert Israel, Sep 05 2024

Keywords

• nonn
• base
• more

Comments

a(n) is the least k for which the concatenation k || k + A376002(n) is prime.

Examples

			a(5) = 929 because A376002(5) = 84 and A032662(84) = 929.  Thus 84 + 929 = 1013, the concatenation 9291013 is prime, the concatenations k || k+84 are composite for 1 <= k < 929, and for every m < 84 there is k < 929 where k || k+m is prime.
		

Crossrefs

Cf. A032662, A376002.

Programs

Maple

tcat:= (a, b) -> a*10^(1+ilog10(b))+b:
f:= proc(n) local k, k0, d;
  for d from ilog10(n)+1 do
    if igcd(10^d+1, n) = 1 then
      k0:= max(1, 10^(d-1)-n);
      if (k0+n)::even then k0:= k0+1 fi;
      for k from k0 to 10^d-n-1 by 2 do
        if isprime(tcat(k, k+n)) then return k fi
   od fi od
end proc:
V:= NULL: m:= 0: count:= 0:
for i from 1 while count < 11 do
  v:= f(i);
  if v > m then
    count:= count+1; m:= v; V:= V, v;
  fi;
od:
V;

Formula

a(n) = A032662(A376002(n)).