A376002 Positions of records in A032662.

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

Offset: 1

Author

Robert Israel, Sep 05 2024

Keywords

• nonn
• base
• more

Comments

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

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

Examples

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

Crossrefs

Cf. A032662, A376006.

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:
R:= 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; R:= R,i;
  fi;
od:
R;