A327133 The difference between 10^n and the lesser of the twin primes immediately before.

5, 29, 119, 71, 11, 41, 29, 413, 809, 299, 239, 41, 1511, 29, 2033, 359, 1193, 1073, 1499, 2261, 5003, 2429, 1793, 4331, 833, 5879, 359, 779, 2813, 1061, 2099, 1811, 3281, 5201, 533, 5483, 1679, 1421, 26801, 12089, 2843, 27773, 9641, 10841, 4763, 2129, 1019, 20531, 8519, 14339

Offset: 1

Author

Robert G. Wilson v, Nov 28 2019

Keywords

• nonn

Comments

All terms are congruent to 5 (mod 6).

Records: 5, 29, 119, 413, 809, 1511, 2033, 2261, 5003, 5879, 26801, ..., 37058441, ... - Robert G. Wilson v, Dec 10 2019

Examples

			a(1) = 5 because the greatest twin prime pair less than 10 is {5, 7};
a(2) = 29 since the greatest 2-digit twin prime pair is {71, 73};
a(3) = 119 since the greatest 3-digit twin prime pair is {881, 883}; etc.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1250

Crossrefs

Cf. A011557, A092250.

Programs

Maple

f:= proc(n) local w,p,q;
w:= 10^n; q:= w;
do
  p:= q;
  q:= prevprime(p);
  if p-q = 2 then return w-q fi;
od
end proc:
map(f, [$1..100]); # Robert Israel, Nov 28 2019

Mathematica

p[n_] := Block[{d = PowerMod[10, n, 6]}, 10^n - NestWhile[# -6 &, 10^n -d -1, !PrimeQ[#] || !PrimeQ[# +2] &]]; Array[p, 50] (* updated Nov 29 2019 *)

PARI

prectwin(n)=n++; while(!isprime(2+n=precprime(n-1)),); n
a(n)=10^n - prectwin(10^n) \\ Charles R Greathouse IV, Nov 28 2019

Formula

a(n) = A011557(n) - A092250(n).